Crop selection under price and yield fluctuation Analysis of

agro-economic time series from South Korea

Heera Leeablowast Christina Bognerc Saem Leea Thomas Koellnera

aProfessorship of Ecological Services Faculty of Biology Chemistry and Earth Sciences BayCEERUniversity of Bayreuth Universitaetsstrasse 30 95440 Bayreuth Germany

bFaculty of Agriculture Land use Modelling and Ecosystem Services University of Bonn Nussallee 153115 Bonn Germany

cEcological Modelling BayCEER University of Bayreuth Dr-Hans-Frisch-Strasse 1ndash3 95448 BayreuthGermany

Abstract

Temporal fluctuations of crop price and yield can have a strong influence on farmersrsquo revenueUnder uncertainty farmersrsquo crop selection on ndash what to cultivate and how much of their landto allocate to different cropsndash is of crucial importance to secure their revenue as well as relatedecosystem services Multi-crop farming can be seen as a strategy to mitigate uncertaintiesthat farmers face In this study we used Singular Spectrum Analysis (SSA) to quantify thefluctuations of crop price and yield for single and multiple crop selections in South KoreaFurthermore risk adjusted revenue of each crop selection was analysed using the Sharperatio We constructed three empirical crop portfolios containing one three and five cropsFor the single crop farming six main crops in South Korea were analysed and householddata were used to build empirical crop portfolios Our results showed that revenue from ricefarming was the most stable whereas it fluctuated strongly for pepper However growingrice provided the lowest revenue and farmers who cultivate multiple crops might as muchas double their revenue compared to rice farming Diversified crop farming can be a meansof enhancing revenue The biggest part of fluctuations in portfolios with several crops wasseasonal which might be mitigated by planning in advance The artificial stability of riceprice was due to policy intervention However it should be noted that the rice policy hasbeen reformed and a high protection for domestic rice farming would no longer last in thefuture in South Korea These results might have practical consequences for farmersrsquo decisionmaking on crop selection as well as for agricultural policy

Keywords Crop choice Crop portfolio Time series analysis Fluctuation analysisSingular Spectrum Analysis (SSA)

1 Introduction

Farmers face various types of risks in agricultural production including price fluctuationsthat can be caused by the dynamics of global economics or climate change (eg Janssen and

lowastCorresponding author Tel +49 228 732925 Fax +49 228 733708Email address hleeuni-bonnde (Heera Lee)

This is an authorrsquos post-print version of the article published in Agricultural Systems 148 1ndash11 (2016)doi101016jagsy201606003

van Ittersum 2007 Fader et al 2013 Feola et al 2015) The tendency of the world pricesfor agricultural commodities to fluctuate over time makes farmers more vulnerable (FAOet al 2011) These fluctuations particularly if large and unexpected can threaten thestability of the farm household income (FAO et al 2011) ndash one of the key indicators to farmwell-being (Mishra et al 2002) Unexpected price volatility and changing environmentalconditions can make it harder for farmers to decide what to cultivate and when to harvestit However these decisions are of crucial importance to secure their revenue and are tightlyrelated to food security1

Accordingly substantial efforts are being directed towards reducing risks and ensuringrevenue stability on the farm household level (Bradshaw et al 2004 Harvey et al 2014Wood et al 2014 Feola et al 2015) Farmers tend to change the type of crops (Wanget al 2010 Klasen et al 2013) land management practices (Wood et al 2014) and thegrowing season (Olesen et al 2011) or extend the scope of income by including off-farmincome (Bradshaw 2004 Harvey et al 2014) for example Several studies pointed out thatdecisions on such practices were influenced by socio-economic background of farmers such asage (Potter and Lobley 1992 van Dusen and Taylor 2005) education (Below et al 2012)and income (Awan et al 2015) As farmers are the main actors who promote agriculturaladaptation and contribute to food security (Kristensen et al 2001 Feola et al 2015) it isimportant to take account of their socio-economic background in relation to their behaviourThis information could help to understand why some take a certain action to adapt tochanges and others omit it (Ilbery 1978 Cutforth et al 2001 Fader et al 2013 Herreroet al 2014 Feola et al 2015)

One of the critical decisions that farmers face is crop selection ndash what to cultivate and howmuch of their land to allocate to different crops (Radulescu et al 2014) As each crop hasdifferent trends of price and yield farmers can reduce risk by cultivating more than one cropCrop diversity can thus be considered as one of the strategies to mitigate the risk and theuncertainties that farmers face (Heady 1952 Bhattacharyya 2008 Rahman 2009 Pellegriniand Tasciotti 2014) through the portfolio effect The portfolio theory (Markowitz 1952)states that the investor can minimise the risk under uncertainty and stabilise the returnby investing in more than one asset It has been applied in various fields of ecologicalstudies such as biodiversity conservation (Koellner and Schmitz 2006 Tilman et al 2006)natural resource management (Halpern et al 2011) and agriculture (Robison and Brake1979 Blank 1990 Lien and Hardaker 2001 Di Falco and Perrings 2005 Radulescu et al2014) Crop diversity can provide farmers with an opportunity to compensate for the lossof revenue caused by the drop of a certain crop price or yield In view of the variability ofprice and yield among different crops crop selection and crop composition in a portfolio istherefore a crucial issue which has a direct impact on the farm household revenue

The influences of crop selection and crop portfolio choice on farm household have beenstudied by several authors For single crop farming Klasen et al (2013) for exampleanalysed the income dynamics caused by crop choice between coffee and cocoa production

1ldquoFood security exists when all people at all times have physical and economic access to sufficient safeand nutritious food to meet their dietary needs and food preferences for an active and healthy liferdquo (RomeDeclaration on World Food Security and World Food Summit Plan of Action 1996)

2

Di Falco and Perrings (2003) studied the effect of crop diversity on mean and variance of in-come in multiple crop farming They found that crop diversity increased the mean of incomeand decreased its variance Guvele (2001) analysed how multiple crop combinations affectthe income variability in Sudan using the mean-variance model Pellegrini and Tasciotti(2014) revealed the positive effect of crop diversification on income by regression analysisHowever most studies do not pass beyond the mean and variance Other studies reportedthe effects of crop diversity on yield however the results were not conclusive Smale et al(1998) for instance used a Just-Pope production function (Just and Pope 1978) to testthe relationship between biotic diversity variables and the mean and variance of yield Theyfound that genealogical variables increased the mean of yield and reduced its variance Cropdiversity also reduced the variance of crop production in Italy (Di Falco and Chavas 2006)and in Ethiopia (Di Falco et al 2010) especially when rainfall was low Di Falco et al(2010) emphasised that crop diversity was crucial under challenging conditions such as lowprecipitation In contrast Carew et al (2009) who used the same Just-Pope approachstated that spatial and temporal diversity had a negative effect on mean yield Most of thepublished studies that examined the impact of crop diversity on yield ignored the temporalfluctuations and concentrated on the mean and the variance To our knowledge only fewstudies considered the temporal structure of the data explicitly except for the use of dummyvariables (Smale et al 1998 Carew et al 2009) However the temporal aspect is crucialfor the stability of farmersrsquo revenue

Detecting and quantifying fluctuations over time in data is the domain of time seriesanalysis It has been applied in various fields of research such as in finance (Liu et al 1999Gopikrishnan et al 2001 Thomakos et al 2002 Kiyono et al 2006) meteorology (Allenand Smith 1994 Talkner and Weber 2000) and oceanography (Vianna and Menezes 2006)However to our knowledge applications to agro-economic time series are rare in the litera-ture Singular spectrum analysis is a model-free method to decompose time series into trendperiodicities and noise (Golyandina et al 2001) Therefore it allows consideration of dif-ferent components of a time series Its data-adaptive character gives it a particular strengthcompared to classical methods like Fourier analysis and makes it suitable to analyse non-linear dynamics (Elsner and Tsonis 1996) Most applications of singular spectrum analysisto economic data focus on forecasting (eg Hassani and Thomakos 2010) In contrast ourgoal is the analysis of different components

Motivated by aforementioned approaches we aim to quantify the temporal fluctuationof crop price and yield for different choices of crops by using singular spectrum analysis Weapply the crop portfolio theory to farmersrsquo crop selection as a strategy to cope with uncer-tainties originated from the market (price uncertainty) and from environmental conditions(yield uncertainty) Our goal is to examine the impact of crop selection and compositionin portfolios on the farm household revenue The case study was based on household datacollected from the Gangwon Province of South Korea and the nation-wide statistical dataWe structured our study into three parts First we investigate a farm household survey offarmersrsquo socio-economic background to understand their crop selection decision and to iden-tify empirical crop portfolios based on crops frequently chosen by farmers This step allowsto compare different crop selections in the study region Second we use singular spectrumanalysis to quantify fluctuations in crop price (1996ndash2011) and yield data (1980ndash2011 formost crops 1965ndash2011 for rice) In this step we quantify the fluctuations of each single crop

3

and how their trends differ from each other Third we finally compare the fluctuations ofsingle crops with those of different empirical crop portfolios constructed in the first step toinvestigate whether crop diversity might stabilise farm revenue

2 Material and methods

21 Study area

The study was conducted in the Gangwon Province of South Korea located in the mid-eastern part of the Korean Peninsula (Supplementary Figure SF1) Eighty-one percentof the total province area is covered with forests and only 10 is agricultural land Thelatter is managed as dry fields (64) and rice paddies (36) (Gangwon Province 2016)The annual average temperature is 116 C (averaged from 1973 to 2009) and the annualaverage precipitation is 1 373 mm More than half of the annual precipitation falls duringthe monsoon period which starts in late June and continues for 30 days on average (Kanget al 2010)

Because the environmental conditions vary from the coastal areas to the mountain re-gions the agricultural practices differ across the province In the north-western part forexample rice farming and livestock production such as pigs and chickens dominate As it isclose to Seoul the capital of South Korea green house farming is also popular The regionsin the North and South-East are close to the coast and visited by many tourists (Gangwon-do Agricultural Research and Extensions Services 2016) This leads to the development ofagritourism where farmers provide the visitors with an opportunity to experience farmingactivities (Hong et al 2003) This can potentially be an income source for farmers Inthe south-western part of the province exporting crop production and off-season fruit farm-ing are the main agricultural activities In contrast in the mountainous area with higheraltitudes dry fields (primarily radish and cabbage) fruit production and rice cultivationdominate (Kim et al 2007)

Due to climate change the regional distribution of major crops is changing Applefarming for example moved northward from the Gyeongbook Province (in the southernpart of South Korea) to the Gangwon Province (Kim et al 2010) Many farmers try newstrategies such as different crop selection to cope with changing farming conditions (Schaefer2013) This adjustment might continue with increasing climate change

22 Farmersrsquo crop selection and empirical crop portfolios

Face-to-face interviews were conducted between 19th of March 2012 and 6th of April 2012targeting farmers who produced crops within the watershed of the Soyang Lake in the Gang-won Province of South Korea Overall 237 farmers were randomly chosen and interviewedhowever 19 farmers were excluded because of incomplete questions and outliers The sur-vey data contained farmersrsquo socio-economic characteristics and how many crops were chosenand cultivated per farm household in this region We used Principal Components Analysis(PCA) to analyse the relationships among these variables and the number of cultivated cropsper farm household PCA is often applied to describe relationships among variables and toidentify patterns among them (Castella and Erout 2002 Lavorel et al 2011) It reduces thedimension of the data by calculating linear combinations of original variables the so calledprincipal components The principal components are ordered by the amount of variance they

4

explain Thus the first principal component explains the largest proportion of variance inthe data set

After analysing the socio-economic condition of farmers we clustered the data by thenumber of crops chosen per farm household to understand how farmers construct their port-folios of crops Farmers were categorised into three groups according to the number of cropsThe most frequently chosen crops within each group were used to construct empirical cropportfolios For instance to determine the crop portfolio for three crops the major cropschosen by the group of farmers who cultivated three or four crops were considered Basedon these categories three empirical crop portfolios were constructed

Subsequently we compared temporal fluctuations of the crop price and yield betweensingle crops and the empirical portfolios In order to detect fluctuations of crop price andyield we analysed nation-wide statistical data (Table ST1 in the online SupplementaryMaterial) The crop price data was provided by the Korea Agro-Fisheries amp Food TradeCorporation (KAMIS) and the Ministry of Food Agriculture Forestry and Fisheries Formost of the analysed crops the monthly price data was available from 1996 to 2011 Annualcrop yield data of the Gangwon Province (mostly 1980 to 2011) was obtained from the cropproduction survey by Korean Statistical Information System (KOSIS) The yield data forLigularia fischeri2 was not available

23 Risk adjusted revenue

The calculation of risk adjusted revenue is motivated by the Sharpe ratio (Sharpe 1994)a measure of risk-adjusted performance of mutual funds We first calculated the nominalrevenue by multiplying the annual yield by the annual mean price of crops Then thenominal revenue was adjusted by the Consumer Price Index (CPI) to get the real revenuewith 2010 being the reference year The CPI for living necessaries were obtained from KOSISSubsequently the Sharpe ratio was calculated as

θp =microp minusRf

σp (1)

where microp is the average performance of the portfolio (ie the mean real revenue see below)Rf is the risk-free rate and σp is the standard deviation of the portfolio We used the Sharperatio to compare investment options to identify which empirical crop portfolio offered themost risk-efficient investment (Elton et al 2007) The higher the Sharpe ratio the lowerthe investment risk in an empirical crop portfolio

In this study we assume that the average performance is only based on the farm revenuewhich is the income that a farmer gains from only actual farming activities off-farm incomeand direct government subsidies were not included We omitted the risk-free rate because itwas the same for all empirical crop portfolios Under these assumptions the risk adjustedrevenue equals the mean real revenue over the period 1996 to 2011 divided by its standarddeviation

2Ligularia fischeri is one of the most popular edible wild plants in South Korea cultivated in mountainousregions like the Gangwon Province It inhabits mostly central and eastern Asia (Brickell 2008)

5

24 Singular Spectrum Analysis

The Singular Spectrum Analysis (SSA) is a method for time series analysis and forecast-ing Since its introduction by Broomhead and King (1986ab) different SSA methodologieshave been developed (eg Golyandina and Zhigljavsky 2013) In this work we use SSA inits basic form (Basic SSA) or repeatedly (Sequential SSA)

Basic SSA is a non-parametric and model-free technique that decomposes a time seriesinto a set of time series such as trend (modulated) periodicities and noise Here we definetrend as any slowly varying time series Thus the main goal of SSA decomposition isobtaining components of the original time series that can be interpreted more easily In thissense Basic SSA can be regarded as a global data-driven frequency decomposition The onlyassumption behind Basic SSA is that the original time series can be represented by a sumof different components (Golyandina and Zhigljavsky 2013) Therefore it can be applied toany time series regardless of its stationarity

We first describe briefly the algorithm of Basic SSA closely following Golyandina andZhigljavsky (2013) and then explain Sequential SSA Basic SSA consists of time series de-composition and reconstruction

Decomposition Consider a real-valued time series XN = (x1 xN) where N is the numberof data points First it is converted into a LtimesK trajectory matrix X

X =

x1 x2 x3 xKx2 x3 x4 xK+1

x3 x4 x5 xK+2

xL xL+1 xL+2 xN

(2)

Its columns consist of lagged vectors of length L of the original time series In other wordsthe trajectory matrix is constructed by moving a window of length L through the time seriesand collecting all K = N minus L+ 1 segments

The second step is the Singular Value Decomposition (SVD) of this trajectory matrix

X = UΛVT (3)

where U and V are the left and right singular vectors respectively and Λ contains d positivesingular values

radicλ1 ge middot middot middot ge

radicλd gt 0 Note that the singular values of X are the square

roots of the eigenvalues of the matrix XXT The collections (radicλi Ui Vi) i = 1 d of

related singular values and singular vectors are called eigentriples

Reconstruction To reconstruct components of the time series we first have to identify whicheigentriples should be grouped together The aim of grouping is to identify the additivecomponents of the time series We partition the set of indices 1 d into m disjointssubsets I1 Im and reconstruct the component time series

XIp =sumiisinIp

radicλiUiV

Ti p = 1 m (4)

6

Thus we obtain the decomposition of the original trajectory matrix

X = XI1 + middot middot middot+ XIm (5)

To recover the additive components of the original time series we have to convert the trajec-tory matrices back to time series by averaging along the secondary diagonals of the matricesXIp

The quality of reconstruction is measured by the ratio of eigenvalues The larger theeigenvalue λi the larger is its ratio λi

sumi λi and the more important is the component for

the reconstruction of the original time series In order for this ratio to be meaningful thetime series should be normalised by subtracting the mean before the SSA (Golyandina andZhigljavsky 2013)

The window length L is a crucial parameter in SSA that strongly influences the decom-position An inappropriate choice of L might lead to separability issues The reconstructedcomponents contain a mixture of different periodicities or periodicities and trend Conse-quently the interpretation of such components is difficult There is no universal rule forchoosing L however some general recommendations exist Usually L le N2 is chosen andmore details can be extracted for larger L If a dominant periodicity T is present (like theyearly cycle) LT should be an integer For small L SSA is equivalent to smoothing witha linear filter of width 2L minus 1 (Golyandina and Zhigljavsky 2013) We chose L = 5 todecompose the short yield time series

The longer price time series showed a complex trend and periodicities For such timeseries the choice of L might become difficult Indeed choosing a large L could mix upperiodicities and trend in the same component On the contrary for a small L periodiccomponents might be inseparable from each other To avoid these separability issues wedecomposed the price time series by Sequential SSA ndash a reiteration of Basic SSA First thetrend is extracted with a small L1 and removed from the original time series Subsequentlythe periodicities are extracted from the residual time series with a larger L2 (Golyandina andZhigljavsky 2013) We chose L1 = 12 and L2 = 48 to extract the trend and the periodicitiesrespectively

Our goal is to compare fluctuations between single crops and crop portfolios It is in-tuitively clear that with respect to revenue stability fluctuations with shorter periods aremore problematic than those with larger periods Therefore we compared the time serieson different time scales For the price data we considered four groups of fluctuations fluc-tuations with periods larger than 24 months (trend) periods of 6ndash24 months (seasonality)3ndash59 months and smaller than 29 months However for the yield data we only distinguishedbetween the trend and the remaining periodicities because the time series were short andconsisted of yearly measurements Different periods for rice and the other crops were chosenas the length of the data was different fluctuations with periods of 23 years and 16 years(trend) for rice and the other crops respectively From now on trend and seasonality willtake on these temporal meanings In the reconstruction step (see above) we grouped theeigentriples according to the dominant periodicity that we calculated from the periodogramof the components A similar approach was used by Mahecha et al (2010) for example tocompare observations with simulated data in biospherendashatmosphere modelling The impor-tance of the fluctuations at a certain time scale is shown by the ratio of the eigenvalues

7

We decomposed the price and the yield of single crops and the price of the crop portfoliosby SSA Because the revenue time series contained only 16 values they were too short foran analysis by SSA All calculations were done in R (R Core Team 2013) using the packageRssa (Korobeynikov 2010 Golyandina and Korobeynikov 2013)

3 Results

31 Farmersrsquo crop selection and empirical crop portfolios

We classified the 218 farmers into three groups based on the number of cultivated cropsGroup 1 included farmers who cultivated one or two crops (n = 44) group 2 those with threeor four crops (n = 100) and group 3 summarised farmers cultivating more than five crops(n = 74) These three groups became the basis of the empirical crop portfolios

The mean age in each group of farmers was 55 54 and 53 for group 1 group 2 and group3 respectively (Table 1) The farming experience increased with the increasing number ofcrops cultivated In group 1 the farm size was smaller compared to the other two groupsThe farm costs (costs of rent labour fertiliser and others) increased with increasing numberof crops which led to lower net income for group 3 with a higher standard deviation Thelevel of education was available as a categorical variable The farmers in group 2 had highereducation compared to the other two groups Note that the total number of farmers in eachgroup was different Among those who had university education 42 of farmers cultivatedmore than five crops

The results of PCA are summarised in Figure 1 and Table 2 The first two principalcomponents (PC) explained approximately 50 of the variance (Supplementary Figure SF6)The first component accounted for 31 of the variance and was positively correlated witheducation and negatively correlated with farming experience The second component ex-plained 189 of the variance and was mainly related to the farm size and the number ofcrops Subsidy was negatively related to PC 2 and had thus an opposite effect comparedto the farm size and the number of crops In other words PC 1 distinguished farmers withmore education and less farming experience from those with less education and more farmingexperience as the main source of variability in the socio-economic background of farmers PC2 contrasted farmers with large farms growing many crops and having less subsidies to thosewith smaller farms and less grown crops having larger subsidies The additional informationregarding the farming management type (eg organic farming partially converted farmingand conventional farming) is supplied in the Supplementary Figure SF2

In total 83 types of crops were cultivated in the watershed of the Soyang Lake in theGangwon Province However 93 of the farmers cultivated one or more crops out of theseven main ones (Table 3) Maize and cabbage shared the same rank However becausemaize is one of the forage crops in South Korea the market conditions differ from othercrops and we excluded it from further analysis Note that in the survey farmers recorded allcrops they planted Therefore the total number of crops and the total number of farmersdiffer

The most critical part of building the empirical crop portfolios was to choose the crops andto decide on their relative contribution In each group of farmers we have selected those whocultivated the smallest number of crops namely one three and five The single crop farmingwas the basis for the comparison Subsequently three- and five-crop portfolios were chosen

8

Tab

le1

Des

crip

tive

stati

stic

sof

farm

ersrsquo

chara

cter

isti

csin

each

gro

up

Gro

up

1a

Gro

up

2b

Gro

up

3c

Tota

l

Conti

nu

ou

sva

riab

les

Aver

age

(sta

nd

ard

dev

iati

on)

Age

(yea

rs)

552

(10

5)54

2(9

8)

539

(82

)54

3(9

4)

Far

min

gex

per

ien

ce(y

ears

)26

6(1

32)

279

(13

2)29

9(1

38)

283

(13

4)F

arm

Siz

e(h

a)2

2(3

3)

31

(32

)3

8(3

9)

32

(35

)T

otal

Cos

tp

erfa

rm(1

00

00

KR

Wd)

121

9(1

691

)3

114

(33

94)

441

5(5

019

)3

165

(39

48)

Rev

enu

ep

erfa

rm(1

000

0K

RW

)3

286

(54

11)

529

0(6

788

)6

363

(54

34)

524

1(6

157

)N

etin

com

ep

erfa

rm(1

00

00K

RW

)2

066

(40

79)

217

6(4

612

)1

947

(37

85)

207

6(4

220

)

Cate

gori

cal

vari

able

sF

requ

ency

(w

ith

inea

chgr

oup

)E

du

cati

onP

rim

ary

school

13(2

95

)26

(26

0)

27(3

65

)66

(30

3)

Sec

on

dary

sch

ool

10(2

27

)38

(38

0)

22(2

97

)70

(32

1)

Hig

hsc

hool

15(3

41

)31

(31

0)

17(2

30

)63

(28

9)

Un

iver

sity

6(1

36

)5

(50

)

8(1

08

)

19(8

7

)

aNumber

ofcrops=

1or2

bNumber

ofcrops=

3or4

cNumber

ofcropsge

5d10000KRW

=853USD

in30th

July

2015

9

minus2 minus1 0 1 2

minus2

0minus

10

00

05

10

PC 1 (31 explained variance)

PC

2 (

189

e

xpla

ined

var

ianc

e)

Education

Age

Farming experience

Farm size (ha)

Number of crops

Subsidy (per ha)

Net income

1minus2 crops3minus4 cropsgt 4 crops

Figure 1 Principal Component Analysis of farmersrsquo characteristics Arrows show original variables Thedirection and the length of the arrows show the correlation between the original variables and the principalcomponents The more an arrow is parallel to the axis the more the original variable is related to thisparticular principal component

Table 2 Loadings from PCA

PC 1 PC 2 PC 3 PC 4 PC 5

Education 0564 0130Age ndash0534 ndash0237 0119 ndash0136 0248Farming experience ndash0569 ndash0218Farm size (ha) 0700 ndash0611Number of crops 0499 ndash0601 0151 0597Subsidy (per ha) 0154 ndash0273 ndash0653 ndash0636 ndash0249Net income 0181 0348 0445 ndash0708 0356

10

Table 3 Number of farmers cultivating the eight main crops in the watershed of the Soyang Lake in theGangwon Province

Rank Crop Number of farmers

1 Pepper 1332 Potato 1163 Beans 904 Ligularia fischeri 645 Rice 596 Radish 527 Cabbage 427 Maize 42

as they were the majorities in each group Then we looked at the most selected crops by eachgroup of farmers Rice was the most frequently cultivated crop by farmers who cultivated asingle crop However as rice is the main staple grain in South Korea rice is highly subsidisedby the government (Korea Rural Economic Institute 2015) which might lead to differentprice conditions compared to the other single crops Therefore we decided not to have riceas a representative crop for the single crop farming but compared all six chosen crops Inthe second group 50 farmers grew three crops most frequently beans pepper and cabbageFinally in the last group among the 25 farmers with five crops potato pepper beanscabbage and Ligularia fischeri dominated However because Ligularia fischeri was relativelynewly introduced to consumers the price data contained large and regularly occurring gaps(Supplementary Table ST1) Therefore SSA could not be carried out for this crop As analternative we have included radish in the five-crop portfolio as the sixth most frequentlychosen crop by farmers who grew five crops We calculated the relative proportions of thesethree or five main crops and composed the empirical crop portfolios as follows

(1) Single crop farming six major crops (100)

(2) Three-crop portfolio beans (350) pepper (325) and cabbage (325)

(3) Five-crop portfolio potato (290) pepper (277) beans (174) cabbage (144)and radish (115)

32 Crop price fluctuations

321 Single crops

Figure 2 shows the variabilities of crop price fluctuations among six main crops in theGangwon Province of South Korea The visual comparison of price data showed that the riceprice was extremely stable compared to any other analysed crops during the study period(Figure 2 and Supplementary Figure SF3 for non-normalised price data) Because rice is themost important cereal crop in South Korea (Korea Rural Economic Institute 2015) severalpolicy instruments such as government buffer stock schemes and direct payments were usedto stabilise the rice price (Park et al 2010) Even though the price for beans was alsorelatively stable a sharp increase was registered in 2004 The price for beans in South Koreais highly dependent on foreign trade and is directly influenced by the global market (OECD

11

Year

Nor

mal

ized

pric

e (K

RW

kg)

minus40

000

2000

6000

1996 1998 2000 2002 2004 2006 2008 2010 2012

ricebeans

potatoradisch

cabbagepepper

Ligularia fischeri

Year

Nor

mal

ized

yie

ld (

ton

ha)

minus15

minus10

minus5

05

1015

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

rice beans potato radisch cabbage pepper

Figure 2 The variability of the normalised crop price (left) and the normalised yield (right) over the analysedperiod The respective mean was subtracted from each time series

2008) Because the US soybean crop yield in 2003 has been the lowest since 1992 theprice in 2004 increased dramatically (USDA 2007) Similarly a large price rise for cabbagewas observed in 2010 although for a different reason (Supplementary Figure SF3 (e) andFigure 2) Due to bad weather in 2010 the supply of cabbage did not meet the demand(Kwon 2012) In comparison to rice and beans the prices for pepper and Ligularia fischerifluctuated strongly

Figure 3 shows the results of the SSA decomposition of the crop prices We consideredfour time scales of fluctuations and evaluated their importance by the ratio of the eigenvalues(cf numbers in parenthesis in Figure 3) These numbers show how much each time scalecontributes to the reconstruction of the original time series We associate the periodicitiesof 24 months and more with a trend and those of 6ndash24 months with seasonal fluctuationsThe third (3ndash59 months) and the fourth (lt 29 months) time scales are however too shortto be interpreted

The prices for rice and beans showed a large contribution of the trend (701 and 546respectively) and a minor one on the smallest time scale (26 and 4 respectively) Thisconfirms the visual impression of stability in Figure 2 Except for rice the crop price datashowed considerable seasonal patterns with the ratio of eigenvalues exceeding 30 Radishand pepper exhibited an especially strong seasonal fluctuation namely 436 and 426respectively Compared to rice and beans cabbage and pepper had a substantial contributionto fluctuations at the smallest time scale (124 and 175 respectively)

322 Crop portfolios

The thee-crop portfolio consisted of beans (35) pepper (325) and cabbage (325)(Figure 4 (a)) The SSA of single crops (Figure 3) showed that the bean price was one ofthe least fluctuating and dominated by the trend whilst pepper and cabbage exhibited alarge seasonal variation The combination of them increased the contribution of the trend(compared to pepper) and decreased the importance of seasonal fluctuations (compared topepper and cabbage) (Figure 4 (a)) However in comparison to the trend-dominated beanprice the fluctuations on all but the largest time scale (trend) increased

The five-crop portfolio included potato (29) pepper (277) beans (174) cabbage(144) and radish (115) (Figure 4 (b)) Compared to the trend-dominated bean price

12

1600

1800

2000

original data gt 24 months (701)(a)

Time

minus50

50

6minus24 months (183)

Time

minus20

20

3minus59 months (89)

Time

minus10

515lt 29 months (26)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

5000

8000

original data gt 24 months (546)(b)

Time

minus20

0020

006minus24 months (303)

Time

minus20

040

0

3minus59 months (111)

Time

minus20

00

200

lt 29 months (4)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

050

015

0025

00

original data gt 24 months (314)(c)

Time

minus40

040

06minus24 months (357)

Time

minus30

030

0 3minus59 months (237)

Time

minus10

020

0lt 29 months (92)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500 original data gt 24 months (238)(d)

Time

minus20

040

06minus24 months (436)

Time

minus20

020

0 3minus59 months (232)

Time

minus10

010

0lt 29 months (95)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500

original data gt 24 months (252)(e)

Time

minus50

050

0

6minus24 months (39)

Time

minus20

020

0 3minus59 months (234)

Time

minus20

020

0

lt 29 months (124)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

6000

1200

0 original data gt 24 months (122)(f)

Time

minus40

0040

006minus24 months (426)

Time

minus20

0020

00 3minus59 months (277)

Time

minus20

0020

00lt 29 months (175)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 3 SSA decomposition of the crop prices (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper Four groups of fluctuation were considered larger than 24 months (trend) 6ndash24 months (sea-sonality) 3ndash59 months smaller than 29 months The number in parenthesis shows the ratio of eigenvaluesThe trend component contains the mean the others show the variability around it

13

1000

3000

5000

original data gt 24 months (239)(a)

Time

minus20

0020

006minus24 months (352)

Time

minus50

050

0 3minus59 months (259)

Timeminus

400

400lt 29 months (15)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

1000

3000

5000

original data gt 24 months (204)(b)

Time

minus20

0020

006minus24 months (408)

Time

minus50

050

0 3minus59 months (236)

Time

minus40

040

0lt 29 months (152)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 4 SSA decomposition of the portfolio prices (a) three-crops portfolio (beans (350) pepper (325)and cabbage (325)) and (b) five-crops portfolio (potato (29) pepper (277) beans (174) cabbage(144) and radish (115))For both portfolio four periods of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it

the contribution of the trend decreased from 546 to 204 Additionally the contributionof the seasonal fluctuation remained comparable to the other crops that have a strong sea-sonal pattern In summary the results of SSA decomposition were similar to the portfoliocomposed of three crops Indeed the summed contributions of the larger time scales (trendand seasonality) as well as those on the smaller time scales differed only slightly

33 Crop yield fluctuations

An in-depth analysis of seasonality was not possible because the time series of yieldconsisted of annual measurements Therefore we only extracted the trend and calculatedthe dominant frequency of the remaining periodicities (Figure 5) The result of SSA showedthat the contribution of the trend varied from 333 to 665 Accordingly the importanceof periodicities ranged from 335 to 667 Their dominant frequency covered 25 years to107 years

In general crop yield had an upwards trend during the analysed period except forradish and cabbage (Figure 5) Four of the six analysed crops namely rice beans potatoand pepper showed increasing trends in the yields In contrast the yield of radish andcabbage had decreased during the 23-year analysed period There were more negative thanpositive extreme values outside the range of the standard deviation of the trend Additionallythe amplitude of negative values was often larger than that of positive values (Figure 5)Interestingly large negative values occurred in different years for different crops In 1980and 1993 for example the rice yield decreased sharply whereas there was a relatively high

14

23

45

6

original data trend (457)(a)

Time

minus2

01

2

25 years (543)

1965 1975 1985 1995 2005

Yie

ld (

ton

ha)

Year

10

12

14

16

18

20

original data trend (333)(b)

Time

minus0

30

00

3

4 years (667)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

1015

2025

3035

40 original data trend (424)(c)

Time

minus10

0527 years (576)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3034

3842 original data trend (349)

(d)

Time

minus6

04

8

46 years (651)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3540

4550

5560 original data trend (344)

(e)

Time

minus10

0523 years (656)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

24

68

1012 original data trend (665)

(f)

Time

minus3

minus1

13

107 years (335)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

Figure 5 SSA decomposition of the crop yield (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper The number in parenthesis shows the ratio of eigenvalues The trend component contains themean the others show the variability around it The yellow area shows plusmn standard deviation around thetrend component Note that the time scale is years and not months as for the price data Fluctuations withperiods of 23 years and 16 years (trend) were chosen for rice and the other crops respectively

15

Year

Rea

l Rev

enue

(M

illio

n K

RW

haminus1

year

minus1)

020

4060

1996 1998 2000 2002 2004 2006 2008 2010

ricebeans

potatoradisch

cabbagepepper

threeminuscrop portfoliofiveminuscrop portfolio

Figure 6 Real revenue for single crops and the empirical crop portfolios

yield in potato in the same year In 1996 the radish yield was very low and the rice yieldmoderately high (See Figure 5 and Supplementary Figure SF4)

The sharp drops of yield often followed damages caused by unusual weather eventsEspecially in 1980 the rice yield reached only 587 of the target yield of South Koreadue to low temperature (Park et al 2010) In 1987 and 2010 radish and cabbage werealso influenced by bad weather (Kwon 2012) Frequent rain and lack of sunlight duringseeding period harmed stabilising seeds (Han and Kim 2010) In addition the yield ofradish and cabbage has declined as the consumption decreases and imports increase (KoreaRural Economic Institute 2015) Actually the import of cabbage has increased since 2003and westernised eating habits of South Koreans has decreased its consumption by 2 peryear since 2002 (Korea Rural Economic Institute 2015)

34 Risk adjusted revenue

The revenue and the Sharpe ratio for each crop portfolio are depicted in Figure 6 andTable 4 The Sharpe ratio is often used to assess the portfolio performance (Blank 1990Roche and McQuinn 2004 Gaydon et al 2012) For example Roche and McQuinn (2004)calculated the Sharpe ratio for the farm land allocation portfolio for grains and Gaydon et al(2012) used it for comparing water management options and their contribution to the farmincome

Figure 6 shows the temporal change of the real revenue of single crops and three-and five-crop portfolios Large differences between the six main crops were observed Rice and beansshowed a stable but the smallest and decreasing revenue compared to the other crops overthe analysed period Pepper showed the highest revenue with the highest standard deviation(Table 4) In the portfolio the mean revenue doubled or tripled and the standard deviationincreased with the number of crops compared to rice and bean single crop farming Althoughthe mean revenue of the crop portfolios was smaller compared to potato and pepper itsstandard deviation decreased The difference between the three- and the five-crop portfoliosin mean and standard deviation was only minor

16

Table 4 Risks adjusted revenue for the analysed period from 1996 to 2011

Crop selection Mean (million KRW) SD Sharpe ratio

Single croprice 1085 173 627

beans 596 175 340potato 3092 770 401radish 1476 298 495

cabbage 2288 435 526pepper 3294 1420 232

three-crop portfolio 2023 532 380five-crop portfolio 2412 560 430

4 Discussion

An advantage of decomposing the time series is that we can not only identify the mostfluctuating crop over time but also quantify different components of fluctuations in eachcrop Fluctuations on larger time scales (trend and seasonality) are easier for farmers toface than short-time variations which are more difficult to address in the planning processIn order to distinguish four time scales of fluctuations in each crop selection we calculatedthe ratio of eigenvalue for each time scale The ratio of eigenvalue stands for the quality ofthe reconstruction of the original time series by a certain component The larger this ratiothe more important the component will be for the reconstruction Among four time scalesthe first and the second scales can be interpreted as trend and seasonality respectively thethird and the fourth scales however were too short to be identified

Farmersrsquo decision on which crop to grow how to allocate the land to grow multiple cropsand when to harvest and sell them plays a crucial role to secure their revenue (Fafchamps1992 Kantanantha et al 2010 Klasen et al 2013) Our result showed that each crop had adifferent fluctuation pattern that highly influenced the farm revenue depending on farmersrsquocrop selection The sum of the first two ratios of eigenvalues for crop price ranged from 548(pepper) to 884 (rice) The larger the contribution of trend and seasonality the less short-time variability is contained in the data Four of the six analysed crops contained notableseasonal patterns The SSA of the three- and the five-crop portfolios also revealed thatimportant seasonal variation still remained in the monthly price data Therefore seasonalityprobably has an important impact on farmersrsquo decisions regarding the times for harvestingor marketing of their crops

The risk adjusted revenue calculated with the Sharpe ratio allows us to compare how muchrevenue standardised per 1 of revenue can be guaranteed for farmers in each crop selectionThe combination of these methods provides more information to support farmersrsquo decision oncrop selection Although the results of SSA and the Sharpe ratio showed that rice and beanfarming were the most stable they provided the lowest revenue The revenue of the three-and the five-crop portfolios was more than two times larger than in rice farming howeverat the same time the standard deviation tripled (Table 4) It indicates that the diversified

17

Time

Pric

e (U

SDto

n)

500

1000

1500

2000

1996 1998 2000 2002 2004 2006 2008 2010 2012

Korean domestic rice price World rice price

200

600

1000 original data gt 24 months (684)

Time

minus10

050

6minus24 months (154)

Time

minus10

00

100

3minus59 months (107)

Time

minus40

040

lt 29 months (54)

1991 1997 2003 2009 2015

Pric

e (U

SD

ton)

Year

Figure 7 Korean domestic rice price converted in USDton and world rice price in USDton (left) SSAdecomposition of the world rice price (right) Four groups of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it The world rice data was Thailand nominal price quote obtained from the World BankGlobal Economic Monitor (GEM) Commodities The exchange rate from Korean Won to USD for each yearwas obtained from the World Bank World Development Indicators

farming could support larger revenue This is in accordance with the study by Bhattacharyya(2008) who showed that a rice dominated farming system in India was changed to high-valuecrops for larger revenue Furthermore an analysis in Argentina showed that diversifiedfarming increased the mean return on capital with a lower coefficient of variation (Pacın andOesterheld 2014) Hence the multiple crop farming may be a means of enhancing revenue(Ali et al 2004 Winters et al 2006 Pacın and Oesterheld 2014 Rahman and Kazal 2015)However the diversification took place slowly due to agricultural subsidies concentrated ona certain crop such as rice in India (Bhattacharyya 2008) This might also be the case inSouth Korea

To examine the artificial stability of the rice price in South Korea we compared thedomestic rice price with the world rice price in USD (Figure 7) As the exchange rate variesbetween years the domestic rice price converted in USD fluctuated more compared to theone in KRW We refer to the SSA result of the rice price in KRW to keep consistency unlessmentioned While the world rice price increased drastically in 2008 as a result of the oilcrisis (Figure 7 right) the Korean domestic price was not affected by it and remained stable(Figure 3 (a)) Overall rice price in the global market fluctuates more than in the SouthKorean domestic market (Baffes and Cosic 2013) Furthermore the Korean domestic priceis more than double or triple the world price ndash the result of a substantial governmentalsupport (Figure 7 left)

South Korea used to have a higher protection for domestic rice farming mainly throughtariff and non-tariff barriers in comparison to other OECD countries (Aksoy 2005) Amongother conventional crops Korean subsidy policy focuses particularly on rice farming by sup-

18

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

Di Falco and Perrings (2003) studied the effect of crop diversity on mean and variance of in-come in multiple crop farming They found that crop diversity increased the mean of incomeand decreased its variance Guvele (2001) analysed how multiple crop combinations affectthe income variability in Sudan using the mean-variance model Pellegrini and Tasciotti(2014) revealed the positive effect of crop diversification on income by regression analysisHowever most studies do not pass beyond the mean and variance Other studies reportedthe effects of crop diversity on yield however the results were not conclusive Smale et al(1998) for instance used a Just-Pope production function (Just and Pope 1978) to testthe relationship between biotic diversity variables and the mean and variance of yield Theyfound that genealogical variables increased the mean of yield and reduced its variance Cropdiversity also reduced the variance of crop production in Italy (Di Falco and Chavas 2006)and in Ethiopia (Di Falco et al 2010) especially when rainfall was low Di Falco et al(2010) emphasised that crop diversity was crucial under challenging conditions such as lowprecipitation In contrast Carew et al (2009) who used the same Just-Pope approachstated that spatial and temporal diversity had a negative effect on mean yield Most of thepublished studies that examined the impact of crop diversity on yield ignored the temporalfluctuations and concentrated on the mean and the variance To our knowledge only fewstudies considered the temporal structure of the data explicitly except for the use of dummyvariables (Smale et al 1998 Carew et al 2009) However the temporal aspect is crucialfor the stability of farmersrsquo revenue

Detecting and quantifying fluctuations over time in data is the domain of time seriesanalysis It has been applied in various fields of research such as in finance (Liu et al 1999Gopikrishnan et al 2001 Thomakos et al 2002 Kiyono et al 2006) meteorology (Allenand Smith 1994 Talkner and Weber 2000) and oceanography (Vianna and Menezes 2006)However to our knowledge applications to agro-economic time series are rare in the litera-ture Singular spectrum analysis is a model-free method to decompose time series into trendperiodicities and noise (Golyandina et al 2001) Therefore it allows consideration of dif-ferent components of a time series Its data-adaptive character gives it a particular strengthcompared to classical methods like Fourier analysis and makes it suitable to analyse non-linear dynamics (Elsner and Tsonis 1996) Most applications of singular spectrum analysisto economic data focus on forecasting (eg Hassani and Thomakos 2010) In contrast ourgoal is the analysis of different components

Motivated by aforementioned approaches we aim to quantify the temporal fluctuationof crop price and yield for different choices of crops by using singular spectrum analysis Weapply the crop portfolio theory to farmersrsquo crop selection as a strategy to cope with uncer-tainties originated from the market (price uncertainty) and from environmental conditions(yield uncertainty) Our goal is to examine the impact of crop selection and compositionin portfolios on the farm household revenue The case study was based on household datacollected from the Gangwon Province of South Korea and the nation-wide statistical dataWe structured our study into three parts First we investigate a farm household survey offarmersrsquo socio-economic background to understand their crop selection decision and to iden-tify empirical crop portfolios based on crops frequently chosen by farmers This step allowsto compare different crop selections in the study region Second we use singular spectrumanalysis to quantify fluctuations in crop price (1996ndash2011) and yield data (1980ndash2011 formost crops 1965ndash2011 for rice) In this step we quantify the fluctuations of each single crop

3

and how their trends differ from each other Third we finally compare the fluctuations ofsingle crops with those of different empirical crop portfolios constructed in the first step toinvestigate whether crop diversity might stabilise farm revenue

2 Material and methods

21 Study area

The study was conducted in the Gangwon Province of South Korea located in the mid-eastern part of the Korean Peninsula (Supplementary Figure SF1) Eighty-one percentof the total province area is covered with forests and only 10 is agricultural land Thelatter is managed as dry fields (64) and rice paddies (36) (Gangwon Province 2016)The annual average temperature is 116 C (averaged from 1973 to 2009) and the annualaverage precipitation is 1 373 mm More than half of the annual precipitation falls duringthe monsoon period which starts in late June and continues for 30 days on average (Kanget al 2010)

Because the environmental conditions vary from the coastal areas to the mountain re-gions the agricultural practices differ across the province In the north-western part forexample rice farming and livestock production such as pigs and chickens dominate As it isclose to Seoul the capital of South Korea green house farming is also popular The regionsin the North and South-East are close to the coast and visited by many tourists (Gangwon-do Agricultural Research and Extensions Services 2016) This leads to the development ofagritourism where farmers provide the visitors with an opportunity to experience farmingactivities (Hong et al 2003) This can potentially be an income source for farmers Inthe south-western part of the province exporting crop production and off-season fruit farm-ing are the main agricultural activities In contrast in the mountainous area with higheraltitudes dry fields (primarily radish and cabbage) fruit production and rice cultivationdominate (Kim et al 2007)

Due to climate change the regional distribution of major crops is changing Applefarming for example moved northward from the Gyeongbook Province (in the southernpart of South Korea) to the Gangwon Province (Kim et al 2010) Many farmers try newstrategies such as different crop selection to cope with changing farming conditions (Schaefer2013) This adjustment might continue with increasing climate change

22 Farmersrsquo crop selection and empirical crop portfolios

Face-to-face interviews were conducted between 19th of March 2012 and 6th of April 2012targeting farmers who produced crops within the watershed of the Soyang Lake in the Gang-won Province of South Korea Overall 237 farmers were randomly chosen and interviewedhowever 19 farmers were excluded because of incomplete questions and outliers The sur-vey data contained farmersrsquo socio-economic characteristics and how many crops were chosenand cultivated per farm household in this region We used Principal Components Analysis(PCA) to analyse the relationships among these variables and the number of cultivated cropsper farm household PCA is often applied to describe relationships among variables and toidentify patterns among them (Castella and Erout 2002 Lavorel et al 2011) It reduces thedimension of the data by calculating linear combinations of original variables the so calledprincipal components The principal components are ordered by the amount of variance they

4

explain Thus the first principal component explains the largest proportion of variance inthe data set

After analysing the socio-economic condition of farmers we clustered the data by thenumber of crops chosen per farm household to understand how farmers construct their port-folios of crops Farmers were categorised into three groups according to the number of cropsThe most frequently chosen crops within each group were used to construct empirical cropportfolios For instance to determine the crop portfolio for three crops the major cropschosen by the group of farmers who cultivated three or four crops were considered Basedon these categories three empirical crop portfolios were constructed

Subsequently we compared temporal fluctuations of the crop price and yield betweensingle crops and the empirical portfolios In order to detect fluctuations of crop price andyield we analysed nation-wide statistical data (Table ST1 in the online SupplementaryMaterial) The crop price data was provided by the Korea Agro-Fisheries amp Food TradeCorporation (KAMIS) and the Ministry of Food Agriculture Forestry and Fisheries Formost of the analysed crops the monthly price data was available from 1996 to 2011 Annualcrop yield data of the Gangwon Province (mostly 1980 to 2011) was obtained from the cropproduction survey by Korean Statistical Information System (KOSIS) The yield data forLigularia fischeri2 was not available

23 Risk adjusted revenue

The calculation of risk adjusted revenue is motivated by the Sharpe ratio (Sharpe 1994)a measure of risk-adjusted performance of mutual funds We first calculated the nominalrevenue by multiplying the annual yield by the annual mean price of crops Then thenominal revenue was adjusted by the Consumer Price Index (CPI) to get the real revenuewith 2010 being the reference year The CPI for living necessaries were obtained from KOSISSubsequently the Sharpe ratio was calculated as

θp =microp minusRf

σp (1)

where microp is the average performance of the portfolio (ie the mean real revenue see below)Rf is the risk-free rate and σp is the standard deviation of the portfolio We used the Sharperatio to compare investment options to identify which empirical crop portfolio offered themost risk-efficient investment (Elton et al 2007) The higher the Sharpe ratio the lowerthe investment risk in an empirical crop portfolio

In this study we assume that the average performance is only based on the farm revenuewhich is the income that a farmer gains from only actual farming activities off-farm incomeand direct government subsidies were not included We omitted the risk-free rate because itwas the same for all empirical crop portfolios Under these assumptions the risk adjustedrevenue equals the mean real revenue over the period 1996 to 2011 divided by its standarddeviation

2Ligularia fischeri is one of the most popular edible wild plants in South Korea cultivated in mountainousregions like the Gangwon Province It inhabits mostly central and eastern Asia (Brickell 2008)

5

24 Singular Spectrum Analysis

The Singular Spectrum Analysis (SSA) is a method for time series analysis and forecast-ing Since its introduction by Broomhead and King (1986ab) different SSA methodologieshave been developed (eg Golyandina and Zhigljavsky 2013) In this work we use SSA inits basic form (Basic SSA) or repeatedly (Sequential SSA)

Basic SSA is a non-parametric and model-free technique that decomposes a time seriesinto a set of time series such as trend (modulated) periodicities and noise Here we definetrend as any slowly varying time series Thus the main goal of SSA decomposition isobtaining components of the original time series that can be interpreted more easily In thissense Basic SSA can be regarded as a global data-driven frequency decomposition The onlyassumption behind Basic SSA is that the original time series can be represented by a sumof different components (Golyandina and Zhigljavsky 2013) Therefore it can be applied toany time series regardless of its stationarity

We first describe briefly the algorithm of Basic SSA closely following Golyandina andZhigljavsky (2013) and then explain Sequential SSA Basic SSA consists of time series de-composition and reconstruction

Decomposition Consider a real-valued time series XN = (x1 xN) where N is the numberof data points First it is converted into a LtimesK trajectory matrix X

X =

x1 x2 x3 xKx2 x3 x4 xK+1

x3 x4 x5 xK+2

xL xL+1 xL+2 xN

(2)

Its columns consist of lagged vectors of length L of the original time series In other wordsthe trajectory matrix is constructed by moving a window of length L through the time seriesand collecting all K = N minus L+ 1 segments

The second step is the Singular Value Decomposition (SVD) of this trajectory matrix

X = UΛVT (3)

where U and V are the left and right singular vectors respectively and Λ contains d positivesingular values

radicλ1 ge middot middot middot ge

radicλd gt 0 Note that the singular values of X are the square

roots of the eigenvalues of the matrix XXT The collections (radicλi Ui Vi) i = 1 d of

related singular values and singular vectors are called eigentriples

Reconstruction To reconstruct components of the time series we first have to identify whicheigentriples should be grouped together The aim of grouping is to identify the additivecomponents of the time series We partition the set of indices 1 d into m disjointssubsets I1 Im and reconstruct the component time series

XIp =sumiisinIp

radicλiUiV

Ti p = 1 m (4)

6

Thus we obtain the decomposition of the original trajectory matrix

X = XI1 + middot middot middot+ XIm (5)

To recover the additive components of the original time series we have to convert the trajec-tory matrices back to time series by averaging along the secondary diagonals of the matricesXIp

The quality of reconstruction is measured by the ratio of eigenvalues The larger theeigenvalue λi the larger is its ratio λi

sumi λi and the more important is the component for

the reconstruction of the original time series In order for this ratio to be meaningful thetime series should be normalised by subtracting the mean before the SSA (Golyandina andZhigljavsky 2013)

The window length L is a crucial parameter in SSA that strongly influences the decom-position An inappropriate choice of L might lead to separability issues The reconstructedcomponents contain a mixture of different periodicities or periodicities and trend Conse-quently the interpretation of such components is difficult There is no universal rule forchoosing L however some general recommendations exist Usually L le N2 is chosen andmore details can be extracted for larger L If a dominant periodicity T is present (like theyearly cycle) LT should be an integer For small L SSA is equivalent to smoothing witha linear filter of width 2L minus 1 (Golyandina and Zhigljavsky 2013) We chose L = 5 todecompose the short yield time series

The longer price time series showed a complex trend and periodicities For such timeseries the choice of L might become difficult Indeed choosing a large L could mix upperiodicities and trend in the same component On the contrary for a small L periodiccomponents might be inseparable from each other To avoid these separability issues wedecomposed the price time series by Sequential SSA ndash a reiteration of Basic SSA First thetrend is extracted with a small L1 and removed from the original time series Subsequentlythe periodicities are extracted from the residual time series with a larger L2 (Golyandina andZhigljavsky 2013) We chose L1 = 12 and L2 = 48 to extract the trend and the periodicitiesrespectively

Our goal is to compare fluctuations between single crops and crop portfolios It is in-tuitively clear that with respect to revenue stability fluctuations with shorter periods aremore problematic than those with larger periods Therefore we compared the time serieson different time scales For the price data we considered four groups of fluctuations fluc-tuations with periods larger than 24 months (trend) periods of 6ndash24 months (seasonality)3ndash59 months and smaller than 29 months However for the yield data we only distinguishedbetween the trend and the remaining periodicities because the time series were short andconsisted of yearly measurements Different periods for rice and the other crops were chosenas the length of the data was different fluctuations with periods of 23 years and 16 years(trend) for rice and the other crops respectively From now on trend and seasonality willtake on these temporal meanings In the reconstruction step (see above) we grouped theeigentriples according to the dominant periodicity that we calculated from the periodogramof the components A similar approach was used by Mahecha et al (2010) for example tocompare observations with simulated data in biospherendashatmosphere modelling The impor-tance of the fluctuations at a certain time scale is shown by the ratio of the eigenvalues

7

We decomposed the price and the yield of single crops and the price of the crop portfoliosby SSA Because the revenue time series contained only 16 values they were too short foran analysis by SSA All calculations were done in R (R Core Team 2013) using the packageRssa (Korobeynikov 2010 Golyandina and Korobeynikov 2013)

3 Results

31 Farmersrsquo crop selection and empirical crop portfolios

We classified the 218 farmers into three groups based on the number of cultivated cropsGroup 1 included farmers who cultivated one or two crops (n = 44) group 2 those with threeor four crops (n = 100) and group 3 summarised farmers cultivating more than five crops(n = 74) These three groups became the basis of the empirical crop portfolios

The mean age in each group of farmers was 55 54 and 53 for group 1 group 2 and group3 respectively (Table 1) The farming experience increased with the increasing number ofcrops cultivated In group 1 the farm size was smaller compared to the other two groupsThe farm costs (costs of rent labour fertiliser and others) increased with increasing numberof crops which led to lower net income for group 3 with a higher standard deviation Thelevel of education was available as a categorical variable The farmers in group 2 had highereducation compared to the other two groups Note that the total number of farmers in eachgroup was different Among those who had university education 42 of farmers cultivatedmore than five crops

The results of PCA are summarised in Figure 1 and Table 2 The first two principalcomponents (PC) explained approximately 50 of the variance (Supplementary Figure SF6)The first component accounted for 31 of the variance and was positively correlated witheducation and negatively correlated with farming experience The second component ex-plained 189 of the variance and was mainly related to the farm size and the number ofcrops Subsidy was negatively related to PC 2 and had thus an opposite effect comparedto the farm size and the number of crops In other words PC 1 distinguished farmers withmore education and less farming experience from those with less education and more farmingexperience as the main source of variability in the socio-economic background of farmers PC2 contrasted farmers with large farms growing many crops and having less subsidies to thosewith smaller farms and less grown crops having larger subsidies The additional informationregarding the farming management type (eg organic farming partially converted farmingand conventional farming) is supplied in the Supplementary Figure SF2

In total 83 types of crops were cultivated in the watershed of the Soyang Lake in theGangwon Province However 93 of the farmers cultivated one or more crops out of theseven main ones (Table 3) Maize and cabbage shared the same rank However becausemaize is one of the forage crops in South Korea the market conditions differ from othercrops and we excluded it from further analysis Note that in the survey farmers recorded allcrops they planted Therefore the total number of crops and the total number of farmersdiffer

The most critical part of building the empirical crop portfolios was to choose the crops andto decide on their relative contribution In each group of farmers we have selected those whocultivated the smallest number of crops namely one three and five The single crop farmingwas the basis for the comparison Subsequently three- and five-crop portfolios were chosen

8

Tab

le1

Des

crip

tive

stati

stic

sof

farm

ersrsquo

chara

cter

isti

csin

each

gro

up

Gro

up

1a

Gro

up

2b

Gro

up

3c

Tota

l

Conti

nu

ou

sva

riab

les

Aver

age

(sta

nd

ard

dev

iati

on)

Age

(yea

rs)

552

(10

5)54

2(9

8)

539

(82

)54

3(9

4)

Far

min

gex

per

ien

ce(y

ears

)26

6(1

32)

279

(13

2)29

9(1

38)

283

(13

4)F

arm

Siz

e(h

a)2

2(3

3)

31

(32

)3

8(3

9)

32

(35

)T

otal

Cos

tp

erfa

rm(1

00

00

KR

Wd)

121

9(1

691

)3

114

(33

94)

441

5(5

019

)3

165

(39

48)

Rev

enu

ep

erfa

rm(1

000

0K

RW

)3

286

(54

11)

529

0(6

788

)6

363

(54

34)

524

1(6

157

)N

etin

com

ep

erfa

rm(1

00

00K

RW

)2

066

(40

79)

217

6(4

612

)1

947

(37

85)

207

6(4

220

)

Cate

gori

cal

vari

able

sF

requ

ency

(w

ith

inea

chgr

oup

)E

du

cati

onP

rim

ary

school

13(2

95

)26

(26

0)

27(3

65

)66

(30

3)

Sec

on

dary

sch

ool

10(2

27

)38

(38

0)

22(2

97

)70

(32

1)

Hig

hsc

hool

15(3

41

)31

(31

0)

17(2

30

)63

(28

9)

Un

iver

sity

6(1

36

)5

(50

)

8(1

08

)

19(8

7

)

aNumber

ofcrops=

1or2

bNumber

ofcrops=

3or4

cNumber

ofcropsge

5d10000KRW

=853USD

in30th

July

2015

9

minus2 minus1 0 1 2

minus2

0minus

10

00

05

10

PC 1 (31 explained variance)

PC

2 (

189

e

xpla

ined

var

ianc

e)

Education

Age

Farming experience

Farm size (ha)

Number of crops

Subsidy (per ha)

Net income

1minus2 crops3minus4 cropsgt 4 crops

Figure 1 Principal Component Analysis of farmersrsquo characteristics Arrows show original variables Thedirection and the length of the arrows show the correlation between the original variables and the principalcomponents The more an arrow is parallel to the axis the more the original variable is related to thisparticular principal component

Table 2 Loadings from PCA

PC 1 PC 2 PC 3 PC 4 PC 5

Education 0564 0130Age ndash0534 ndash0237 0119 ndash0136 0248Farming experience ndash0569 ndash0218Farm size (ha) 0700 ndash0611Number of crops 0499 ndash0601 0151 0597Subsidy (per ha) 0154 ndash0273 ndash0653 ndash0636 ndash0249Net income 0181 0348 0445 ndash0708 0356

10

Table 3 Number of farmers cultivating the eight main crops in the watershed of the Soyang Lake in theGangwon Province

Rank Crop Number of farmers

1 Pepper 1332 Potato 1163 Beans 904 Ligularia fischeri 645 Rice 596 Radish 527 Cabbage 427 Maize 42

as they were the majorities in each group Then we looked at the most selected crops by eachgroup of farmers Rice was the most frequently cultivated crop by farmers who cultivated asingle crop However as rice is the main staple grain in South Korea rice is highly subsidisedby the government (Korea Rural Economic Institute 2015) which might lead to differentprice conditions compared to the other single crops Therefore we decided not to have riceas a representative crop for the single crop farming but compared all six chosen crops Inthe second group 50 farmers grew three crops most frequently beans pepper and cabbageFinally in the last group among the 25 farmers with five crops potato pepper beanscabbage and Ligularia fischeri dominated However because Ligularia fischeri was relativelynewly introduced to consumers the price data contained large and regularly occurring gaps(Supplementary Table ST1) Therefore SSA could not be carried out for this crop As analternative we have included radish in the five-crop portfolio as the sixth most frequentlychosen crop by farmers who grew five crops We calculated the relative proportions of thesethree or five main crops and composed the empirical crop portfolios as follows

(1) Single crop farming six major crops (100)

(2) Three-crop portfolio beans (350) pepper (325) and cabbage (325)

(3) Five-crop portfolio potato (290) pepper (277) beans (174) cabbage (144)and radish (115)

32 Crop price fluctuations

321 Single crops

Figure 2 shows the variabilities of crop price fluctuations among six main crops in theGangwon Province of South Korea The visual comparison of price data showed that the riceprice was extremely stable compared to any other analysed crops during the study period(Figure 2 and Supplementary Figure SF3 for non-normalised price data) Because rice is themost important cereal crop in South Korea (Korea Rural Economic Institute 2015) severalpolicy instruments such as government buffer stock schemes and direct payments were usedto stabilise the rice price (Park et al 2010) Even though the price for beans was alsorelatively stable a sharp increase was registered in 2004 The price for beans in South Koreais highly dependent on foreign trade and is directly influenced by the global market (OECD

11

Year

Nor

mal

ized

pric

e (K

RW

kg)

minus40

000

2000

6000

1996 1998 2000 2002 2004 2006 2008 2010 2012

ricebeans

potatoradisch

cabbagepepper

Ligularia fischeri

Year

Nor

mal

ized

yie

ld (

ton

ha)

minus15

minus10

minus5

05

1015

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

rice beans potato radisch cabbage pepper

Figure 2 The variability of the normalised crop price (left) and the normalised yield (right) over the analysedperiod The respective mean was subtracted from each time series

2008) Because the US soybean crop yield in 2003 has been the lowest since 1992 theprice in 2004 increased dramatically (USDA 2007) Similarly a large price rise for cabbagewas observed in 2010 although for a different reason (Supplementary Figure SF3 (e) andFigure 2) Due to bad weather in 2010 the supply of cabbage did not meet the demand(Kwon 2012) In comparison to rice and beans the prices for pepper and Ligularia fischerifluctuated strongly

Figure 3 shows the results of the SSA decomposition of the crop prices We consideredfour time scales of fluctuations and evaluated their importance by the ratio of the eigenvalues(cf numbers in parenthesis in Figure 3) These numbers show how much each time scalecontributes to the reconstruction of the original time series We associate the periodicitiesof 24 months and more with a trend and those of 6ndash24 months with seasonal fluctuationsThe third (3ndash59 months) and the fourth (lt 29 months) time scales are however too shortto be interpreted

The prices for rice and beans showed a large contribution of the trend (701 and 546respectively) and a minor one on the smallest time scale (26 and 4 respectively) Thisconfirms the visual impression of stability in Figure 2 Except for rice the crop price datashowed considerable seasonal patterns with the ratio of eigenvalues exceeding 30 Radishand pepper exhibited an especially strong seasonal fluctuation namely 436 and 426respectively Compared to rice and beans cabbage and pepper had a substantial contributionto fluctuations at the smallest time scale (124 and 175 respectively)

322 Crop portfolios

The thee-crop portfolio consisted of beans (35) pepper (325) and cabbage (325)(Figure 4 (a)) The SSA of single crops (Figure 3) showed that the bean price was one ofthe least fluctuating and dominated by the trend whilst pepper and cabbage exhibited alarge seasonal variation The combination of them increased the contribution of the trend(compared to pepper) and decreased the importance of seasonal fluctuations (compared topepper and cabbage) (Figure 4 (a)) However in comparison to the trend-dominated beanprice the fluctuations on all but the largest time scale (trend) increased

The five-crop portfolio included potato (29) pepper (277) beans (174) cabbage(144) and radish (115) (Figure 4 (b)) Compared to the trend-dominated bean price

12

1600

1800

2000

original data gt 24 months (701)(a)

Time

minus50

50

6minus24 months (183)

Time

minus20

20

3minus59 months (89)

Time

minus10

515lt 29 months (26)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

5000

8000

original data gt 24 months (546)(b)

Time

minus20

0020

006minus24 months (303)

Time

minus20

040

0

3minus59 months (111)

Time

minus20

00

200

lt 29 months (4)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

050

015

0025

00

original data gt 24 months (314)(c)

Time

minus40

040

06minus24 months (357)

Time

minus30

030

0 3minus59 months (237)

Time

minus10

020

0lt 29 months (92)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500 original data gt 24 months (238)(d)

Time

minus20

040

06minus24 months (436)

Time

minus20

020

0 3minus59 months (232)

Time

minus10

010

0lt 29 months (95)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500

original data gt 24 months (252)(e)

Time

minus50

050

0

6minus24 months (39)

Time

minus20

020

0 3minus59 months (234)

Time

minus20

020

0

lt 29 months (124)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

6000

1200

0 original data gt 24 months (122)(f)

Time

minus40

0040

006minus24 months (426)

Time

minus20

0020

00 3minus59 months (277)

Time

minus20

0020

00lt 29 months (175)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 3 SSA decomposition of the crop prices (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper Four groups of fluctuation were considered larger than 24 months (trend) 6ndash24 months (sea-sonality) 3ndash59 months smaller than 29 months The number in parenthesis shows the ratio of eigenvaluesThe trend component contains the mean the others show the variability around it

13

1000

3000

5000

original data gt 24 months (239)(a)

Time

minus20

0020

006minus24 months (352)

Time

minus50

050

0 3minus59 months (259)

Timeminus

400

400lt 29 months (15)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

1000

3000

5000

original data gt 24 months (204)(b)

Time

minus20

0020

006minus24 months (408)

Time

minus50

050

0 3minus59 months (236)

Time

minus40

040

0lt 29 months (152)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 4 SSA decomposition of the portfolio prices (a) three-crops portfolio (beans (350) pepper (325)and cabbage (325)) and (b) five-crops portfolio (potato (29) pepper (277) beans (174) cabbage(144) and radish (115))For both portfolio four periods of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it

the contribution of the trend decreased from 546 to 204 Additionally the contributionof the seasonal fluctuation remained comparable to the other crops that have a strong sea-sonal pattern In summary the results of SSA decomposition were similar to the portfoliocomposed of three crops Indeed the summed contributions of the larger time scales (trendand seasonality) as well as those on the smaller time scales differed only slightly

33 Crop yield fluctuations

An in-depth analysis of seasonality was not possible because the time series of yieldconsisted of annual measurements Therefore we only extracted the trend and calculatedthe dominant frequency of the remaining periodicities (Figure 5) The result of SSA showedthat the contribution of the trend varied from 333 to 665 Accordingly the importanceof periodicities ranged from 335 to 667 Their dominant frequency covered 25 years to107 years

In general crop yield had an upwards trend during the analysed period except forradish and cabbage (Figure 5) Four of the six analysed crops namely rice beans potatoand pepper showed increasing trends in the yields In contrast the yield of radish andcabbage had decreased during the 23-year analysed period There were more negative thanpositive extreme values outside the range of the standard deviation of the trend Additionallythe amplitude of negative values was often larger than that of positive values (Figure 5)Interestingly large negative values occurred in different years for different crops In 1980and 1993 for example the rice yield decreased sharply whereas there was a relatively high

14

23

45

6

original data trend (457)(a)

Time

minus2

01

2

25 years (543)

1965 1975 1985 1995 2005

Yie

ld (

ton

ha)

Year

10

12

14

16

18

20

original data trend (333)(b)

Time

minus0

30

00

3

4 years (667)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

1015

2025

3035

40 original data trend (424)(c)

Time

minus10

0527 years (576)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3034

3842 original data trend (349)

(d)

Time

minus6

04

8

46 years (651)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3540

4550

5560 original data trend (344)

(e)

Time

minus10

0523 years (656)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

24

68

1012 original data trend (665)

(f)

Time

minus3

minus1

13

107 years (335)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

Figure 5 SSA decomposition of the crop yield (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper The number in parenthesis shows the ratio of eigenvalues The trend component contains themean the others show the variability around it The yellow area shows plusmn standard deviation around thetrend component Note that the time scale is years and not months as for the price data Fluctuations withperiods of 23 years and 16 years (trend) were chosen for rice and the other crops respectively

15

Year

Rea

l Rev

enue

(M

illio

n K

RW

haminus1

year

minus1)

020

4060

1996 1998 2000 2002 2004 2006 2008 2010

ricebeans

potatoradisch

cabbagepepper

threeminuscrop portfoliofiveminuscrop portfolio

Figure 6 Real revenue for single crops and the empirical crop portfolios

yield in potato in the same year In 1996 the radish yield was very low and the rice yieldmoderately high (See Figure 5 and Supplementary Figure SF4)

The sharp drops of yield often followed damages caused by unusual weather eventsEspecially in 1980 the rice yield reached only 587 of the target yield of South Koreadue to low temperature (Park et al 2010) In 1987 and 2010 radish and cabbage werealso influenced by bad weather (Kwon 2012) Frequent rain and lack of sunlight duringseeding period harmed stabilising seeds (Han and Kim 2010) In addition the yield ofradish and cabbage has declined as the consumption decreases and imports increase (KoreaRural Economic Institute 2015) Actually the import of cabbage has increased since 2003and westernised eating habits of South Koreans has decreased its consumption by 2 peryear since 2002 (Korea Rural Economic Institute 2015)

34 Risk adjusted revenue

The revenue and the Sharpe ratio for each crop portfolio are depicted in Figure 6 andTable 4 The Sharpe ratio is often used to assess the portfolio performance (Blank 1990Roche and McQuinn 2004 Gaydon et al 2012) For example Roche and McQuinn (2004)calculated the Sharpe ratio for the farm land allocation portfolio for grains and Gaydon et al(2012) used it for comparing water management options and their contribution to the farmincome

Figure 6 shows the temporal change of the real revenue of single crops and three-and five-crop portfolios Large differences between the six main crops were observed Rice and beansshowed a stable but the smallest and decreasing revenue compared to the other crops overthe analysed period Pepper showed the highest revenue with the highest standard deviation(Table 4) In the portfolio the mean revenue doubled or tripled and the standard deviationincreased with the number of crops compared to rice and bean single crop farming Althoughthe mean revenue of the crop portfolios was smaller compared to potato and pepper itsstandard deviation decreased The difference between the three- and the five-crop portfoliosin mean and standard deviation was only minor

16

Table 4 Risks adjusted revenue for the analysed period from 1996 to 2011

Crop selection Mean (million KRW) SD Sharpe ratio

Single croprice 1085 173 627

beans 596 175 340potato 3092 770 401radish 1476 298 495

cabbage 2288 435 526pepper 3294 1420 232

three-crop portfolio 2023 532 380five-crop portfolio 2412 560 430

4 Discussion

An advantage of decomposing the time series is that we can not only identify the mostfluctuating crop over time but also quantify different components of fluctuations in eachcrop Fluctuations on larger time scales (trend and seasonality) are easier for farmers toface than short-time variations which are more difficult to address in the planning processIn order to distinguish four time scales of fluctuations in each crop selection we calculatedthe ratio of eigenvalue for each time scale The ratio of eigenvalue stands for the quality ofthe reconstruction of the original time series by a certain component The larger this ratiothe more important the component will be for the reconstruction Among four time scalesthe first and the second scales can be interpreted as trend and seasonality respectively thethird and the fourth scales however were too short to be identified

Farmersrsquo decision on which crop to grow how to allocate the land to grow multiple cropsand when to harvest and sell them plays a crucial role to secure their revenue (Fafchamps1992 Kantanantha et al 2010 Klasen et al 2013) Our result showed that each crop had adifferent fluctuation pattern that highly influenced the farm revenue depending on farmersrsquocrop selection The sum of the first two ratios of eigenvalues for crop price ranged from 548(pepper) to 884 (rice) The larger the contribution of trend and seasonality the less short-time variability is contained in the data Four of the six analysed crops contained notableseasonal patterns The SSA of the three- and the five-crop portfolios also revealed thatimportant seasonal variation still remained in the monthly price data Therefore seasonalityprobably has an important impact on farmersrsquo decisions regarding the times for harvestingor marketing of their crops

The risk adjusted revenue calculated with the Sharpe ratio allows us to compare how muchrevenue standardised per 1 of revenue can be guaranteed for farmers in each crop selectionThe combination of these methods provides more information to support farmersrsquo decision oncrop selection Although the results of SSA and the Sharpe ratio showed that rice and beanfarming were the most stable they provided the lowest revenue The revenue of the three-and the five-crop portfolios was more than two times larger than in rice farming howeverat the same time the standard deviation tripled (Table 4) It indicates that the diversified

17

Time

Pric

e (U

SDto

n)

500

1000

1500

2000

1996 1998 2000 2002 2004 2006 2008 2010 2012

Korean domestic rice price World rice price

200

600

1000 original data gt 24 months (684)

Time

minus10

050

6minus24 months (154)

Time

minus10

00

100

3minus59 months (107)

Time

minus40

040

lt 29 months (54)

1991 1997 2003 2009 2015

Pric

e (U

SD

ton)

Year

Figure 7 Korean domestic rice price converted in USDton and world rice price in USDton (left) SSAdecomposition of the world rice price (right) Four groups of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it The world rice data was Thailand nominal price quote obtained from the World BankGlobal Economic Monitor (GEM) Commodities The exchange rate from Korean Won to USD for each yearwas obtained from the World Bank World Development Indicators

farming could support larger revenue This is in accordance with the study by Bhattacharyya(2008) who showed that a rice dominated farming system in India was changed to high-valuecrops for larger revenue Furthermore an analysis in Argentina showed that diversifiedfarming increased the mean return on capital with a lower coefficient of variation (Pacın andOesterheld 2014) Hence the multiple crop farming may be a means of enhancing revenue(Ali et al 2004 Winters et al 2006 Pacın and Oesterheld 2014 Rahman and Kazal 2015)However the diversification took place slowly due to agricultural subsidies concentrated ona certain crop such as rice in India (Bhattacharyya 2008) This might also be the case inSouth Korea

To examine the artificial stability of the rice price in South Korea we compared thedomestic rice price with the world rice price in USD (Figure 7) As the exchange rate variesbetween years the domestic rice price converted in USD fluctuated more compared to theone in KRW We refer to the SSA result of the rice price in KRW to keep consistency unlessmentioned While the world rice price increased drastically in 2008 as a result of the oilcrisis (Figure 7 right) the Korean domestic price was not affected by it and remained stable(Figure 3 (a)) Overall rice price in the global market fluctuates more than in the SouthKorean domestic market (Baffes and Cosic 2013) Furthermore the Korean domestic priceis more than double or triple the world price ndash the result of a substantial governmentalsupport (Figure 7 left)

South Korea used to have a higher protection for domestic rice farming mainly throughtariff and non-tariff barriers in comparison to other OECD countries (Aksoy 2005) Amongother conventional crops Korean subsidy policy focuses particularly on rice farming by sup-

18

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

and how their trends differ from each other Third we finally compare the fluctuations ofsingle crops with those of different empirical crop portfolios constructed in the first step toinvestigate whether crop diversity might stabilise farm revenue

2 Material and methods

21 Study area

The study was conducted in the Gangwon Province of South Korea located in the mid-eastern part of the Korean Peninsula (Supplementary Figure SF1) Eighty-one percentof the total province area is covered with forests and only 10 is agricultural land Thelatter is managed as dry fields (64) and rice paddies (36) (Gangwon Province 2016)The annual average temperature is 116 C (averaged from 1973 to 2009) and the annualaverage precipitation is 1 373 mm More than half of the annual precipitation falls duringthe monsoon period which starts in late June and continues for 30 days on average (Kanget al 2010)

Because the environmental conditions vary from the coastal areas to the mountain re-gions the agricultural practices differ across the province In the north-western part forexample rice farming and livestock production such as pigs and chickens dominate As it isclose to Seoul the capital of South Korea green house farming is also popular The regionsin the North and South-East are close to the coast and visited by many tourists (Gangwon-do Agricultural Research and Extensions Services 2016) This leads to the development ofagritourism where farmers provide the visitors with an opportunity to experience farmingactivities (Hong et al 2003) This can potentially be an income source for farmers Inthe south-western part of the province exporting crop production and off-season fruit farm-ing are the main agricultural activities In contrast in the mountainous area with higheraltitudes dry fields (primarily radish and cabbage) fruit production and rice cultivationdominate (Kim et al 2007)

Due to climate change the regional distribution of major crops is changing Applefarming for example moved northward from the Gyeongbook Province (in the southernpart of South Korea) to the Gangwon Province (Kim et al 2010) Many farmers try newstrategies such as different crop selection to cope with changing farming conditions (Schaefer2013) This adjustment might continue with increasing climate change

22 Farmersrsquo crop selection and empirical crop portfolios

Face-to-face interviews were conducted between 19th of March 2012 and 6th of April 2012targeting farmers who produced crops within the watershed of the Soyang Lake in the Gang-won Province of South Korea Overall 237 farmers were randomly chosen and interviewedhowever 19 farmers were excluded because of incomplete questions and outliers The sur-vey data contained farmersrsquo socio-economic characteristics and how many crops were chosenand cultivated per farm household in this region We used Principal Components Analysis(PCA) to analyse the relationships among these variables and the number of cultivated cropsper farm household PCA is often applied to describe relationships among variables and toidentify patterns among them (Castella and Erout 2002 Lavorel et al 2011) It reduces thedimension of the data by calculating linear combinations of original variables the so calledprincipal components The principal components are ordered by the amount of variance they

4

explain Thus the first principal component explains the largest proportion of variance inthe data set

After analysing the socio-economic condition of farmers we clustered the data by thenumber of crops chosen per farm household to understand how farmers construct their port-folios of crops Farmers were categorised into three groups according to the number of cropsThe most frequently chosen crops within each group were used to construct empirical cropportfolios For instance to determine the crop portfolio for three crops the major cropschosen by the group of farmers who cultivated three or four crops were considered Basedon these categories three empirical crop portfolios were constructed

Subsequently we compared temporal fluctuations of the crop price and yield betweensingle crops and the empirical portfolios In order to detect fluctuations of crop price andyield we analysed nation-wide statistical data (Table ST1 in the online SupplementaryMaterial) The crop price data was provided by the Korea Agro-Fisheries amp Food TradeCorporation (KAMIS) and the Ministry of Food Agriculture Forestry and Fisheries Formost of the analysed crops the monthly price data was available from 1996 to 2011 Annualcrop yield data of the Gangwon Province (mostly 1980 to 2011) was obtained from the cropproduction survey by Korean Statistical Information System (KOSIS) The yield data forLigularia fischeri2 was not available

23 Risk adjusted revenue

The calculation of risk adjusted revenue is motivated by the Sharpe ratio (Sharpe 1994)a measure of risk-adjusted performance of mutual funds We first calculated the nominalrevenue by multiplying the annual yield by the annual mean price of crops Then thenominal revenue was adjusted by the Consumer Price Index (CPI) to get the real revenuewith 2010 being the reference year The CPI for living necessaries were obtained from KOSISSubsequently the Sharpe ratio was calculated as

θp =microp minusRf

σp (1)

where microp is the average performance of the portfolio (ie the mean real revenue see below)Rf is the risk-free rate and σp is the standard deviation of the portfolio We used the Sharperatio to compare investment options to identify which empirical crop portfolio offered themost risk-efficient investment (Elton et al 2007) The higher the Sharpe ratio the lowerthe investment risk in an empirical crop portfolio

In this study we assume that the average performance is only based on the farm revenuewhich is the income that a farmer gains from only actual farming activities off-farm incomeand direct government subsidies were not included We omitted the risk-free rate because itwas the same for all empirical crop portfolios Under these assumptions the risk adjustedrevenue equals the mean real revenue over the period 1996 to 2011 divided by its standarddeviation

2Ligularia fischeri is one of the most popular edible wild plants in South Korea cultivated in mountainousregions like the Gangwon Province It inhabits mostly central and eastern Asia (Brickell 2008)

5

24 Singular Spectrum Analysis

The Singular Spectrum Analysis (SSA) is a method for time series analysis and forecast-ing Since its introduction by Broomhead and King (1986ab) different SSA methodologieshave been developed (eg Golyandina and Zhigljavsky 2013) In this work we use SSA inits basic form (Basic SSA) or repeatedly (Sequential SSA)

Basic SSA is a non-parametric and model-free technique that decomposes a time seriesinto a set of time series such as trend (modulated) periodicities and noise Here we definetrend as any slowly varying time series Thus the main goal of SSA decomposition isobtaining components of the original time series that can be interpreted more easily In thissense Basic SSA can be regarded as a global data-driven frequency decomposition The onlyassumption behind Basic SSA is that the original time series can be represented by a sumof different components (Golyandina and Zhigljavsky 2013) Therefore it can be applied toany time series regardless of its stationarity

We first describe briefly the algorithm of Basic SSA closely following Golyandina andZhigljavsky (2013) and then explain Sequential SSA Basic SSA consists of time series de-composition and reconstruction

Decomposition Consider a real-valued time series XN = (x1 xN) where N is the numberof data points First it is converted into a LtimesK trajectory matrix X

X =

x1 x2 x3 xKx2 x3 x4 xK+1

x3 x4 x5 xK+2

xL xL+1 xL+2 xN

(2)

Its columns consist of lagged vectors of length L of the original time series In other wordsthe trajectory matrix is constructed by moving a window of length L through the time seriesand collecting all K = N minus L+ 1 segments

The second step is the Singular Value Decomposition (SVD) of this trajectory matrix

X = UΛVT (3)

where U and V are the left and right singular vectors respectively and Λ contains d positivesingular values

radicλ1 ge middot middot middot ge

radicλd gt 0 Note that the singular values of X are the square

roots of the eigenvalues of the matrix XXT The collections (radicλi Ui Vi) i = 1 d of

related singular values and singular vectors are called eigentriples

Reconstruction To reconstruct components of the time series we first have to identify whicheigentriples should be grouped together The aim of grouping is to identify the additivecomponents of the time series We partition the set of indices 1 d into m disjointssubsets I1 Im and reconstruct the component time series

XIp =sumiisinIp

radicλiUiV

Ti p = 1 m (4)

6

Thus we obtain the decomposition of the original trajectory matrix

X = XI1 + middot middot middot+ XIm (5)

To recover the additive components of the original time series we have to convert the trajec-tory matrices back to time series by averaging along the secondary diagonals of the matricesXIp

The quality of reconstruction is measured by the ratio of eigenvalues The larger theeigenvalue λi the larger is its ratio λi

sumi λi and the more important is the component for

the reconstruction of the original time series In order for this ratio to be meaningful thetime series should be normalised by subtracting the mean before the SSA (Golyandina andZhigljavsky 2013)

The window length L is a crucial parameter in SSA that strongly influences the decom-position An inappropriate choice of L might lead to separability issues The reconstructedcomponents contain a mixture of different periodicities or periodicities and trend Conse-quently the interpretation of such components is difficult There is no universal rule forchoosing L however some general recommendations exist Usually L le N2 is chosen andmore details can be extracted for larger L If a dominant periodicity T is present (like theyearly cycle) LT should be an integer For small L SSA is equivalent to smoothing witha linear filter of width 2L minus 1 (Golyandina and Zhigljavsky 2013) We chose L = 5 todecompose the short yield time series

The longer price time series showed a complex trend and periodicities For such timeseries the choice of L might become difficult Indeed choosing a large L could mix upperiodicities and trend in the same component On the contrary for a small L periodiccomponents might be inseparable from each other To avoid these separability issues wedecomposed the price time series by Sequential SSA ndash a reiteration of Basic SSA First thetrend is extracted with a small L1 and removed from the original time series Subsequentlythe periodicities are extracted from the residual time series with a larger L2 (Golyandina andZhigljavsky 2013) We chose L1 = 12 and L2 = 48 to extract the trend and the periodicitiesrespectively

Our goal is to compare fluctuations between single crops and crop portfolios It is in-tuitively clear that with respect to revenue stability fluctuations with shorter periods aremore problematic than those with larger periods Therefore we compared the time serieson different time scales For the price data we considered four groups of fluctuations fluc-tuations with periods larger than 24 months (trend) periods of 6ndash24 months (seasonality)3ndash59 months and smaller than 29 months However for the yield data we only distinguishedbetween the trend and the remaining periodicities because the time series were short andconsisted of yearly measurements Different periods for rice and the other crops were chosenas the length of the data was different fluctuations with periods of 23 years and 16 years(trend) for rice and the other crops respectively From now on trend and seasonality willtake on these temporal meanings In the reconstruction step (see above) we grouped theeigentriples according to the dominant periodicity that we calculated from the periodogramof the components A similar approach was used by Mahecha et al (2010) for example tocompare observations with simulated data in biospherendashatmosphere modelling The impor-tance of the fluctuations at a certain time scale is shown by the ratio of the eigenvalues

7

We decomposed the price and the yield of single crops and the price of the crop portfoliosby SSA Because the revenue time series contained only 16 values they were too short foran analysis by SSA All calculations were done in R (R Core Team 2013) using the packageRssa (Korobeynikov 2010 Golyandina and Korobeynikov 2013)

3 Results

31 Farmersrsquo crop selection and empirical crop portfolios

We classified the 218 farmers into three groups based on the number of cultivated cropsGroup 1 included farmers who cultivated one or two crops (n = 44) group 2 those with threeor four crops (n = 100) and group 3 summarised farmers cultivating more than five crops(n = 74) These three groups became the basis of the empirical crop portfolios

The mean age in each group of farmers was 55 54 and 53 for group 1 group 2 and group3 respectively (Table 1) The farming experience increased with the increasing number ofcrops cultivated In group 1 the farm size was smaller compared to the other two groupsThe farm costs (costs of rent labour fertiliser and others) increased with increasing numberof crops which led to lower net income for group 3 with a higher standard deviation Thelevel of education was available as a categorical variable The farmers in group 2 had highereducation compared to the other two groups Note that the total number of farmers in eachgroup was different Among those who had university education 42 of farmers cultivatedmore than five crops

The results of PCA are summarised in Figure 1 and Table 2 The first two principalcomponents (PC) explained approximately 50 of the variance (Supplementary Figure SF6)The first component accounted for 31 of the variance and was positively correlated witheducation and negatively correlated with farming experience The second component ex-plained 189 of the variance and was mainly related to the farm size and the number ofcrops Subsidy was negatively related to PC 2 and had thus an opposite effect comparedto the farm size and the number of crops In other words PC 1 distinguished farmers withmore education and less farming experience from those with less education and more farmingexperience as the main source of variability in the socio-economic background of farmers PC2 contrasted farmers with large farms growing many crops and having less subsidies to thosewith smaller farms and less grown crops having larger subsidies The additional informationregarding the farming management type (eg organic farming partially converted farmingand conventional farming) is supplied in the Supplementary Figure SF2

In total 83 types of crops were cultivated in the watershed of the Soyang Lake in theGangwon Province However 93 of the farmers cultivated one or more crops out of theseven main ones (Table 3) Maize and cabbage shared the same rank However becausemaize is one of the forage crops in South Korea the market conditions differ from othercrops and we excluded it from further analysis Note that in the survey farmers recorded allcrops they planted Therefore the total number of crops and the total number of farmersdiffer

The most critical part of building the empirical crop portfolios was to choose the crops andto decide on their relative contribution In each group of farmers we have selected those whocultivated the smallest number of crops namely one three and five The single crop farmingwas the basis for the comparison Subsequently three- and five-crop portfolios were chosen

8

Tab

le1

Des

crip

tive

stati

stic

sof

farm

ersrsquo

chara

cter

isti

csin

each

gro

up

Gro

up

1a

Gro

up

2b

Gro

up

3c

Tota

l

Conti

nu

ou

sva

riab

les

Aver

age

(sta

nd

ard

dev

iati

on)

Age

(yea

rs)

552

(10

5)54

2(9

8)

539

(82

)54

3(9

4)

Far

min

gex

per

ien

ce(y

ears

)26

6(1

32)

279

(13

2)29

9(1

38)

283

(13

4)F

arm

Siz

e(h

a)2

2(3

3)

31

(32

)3

8(3

9)

32

(35

)T

otal

Cos

tp

erfa

rm(1

00

00

KR

Wd)

121

9(1

691

)3

114

(33

94)

441

5(5

019

)3

165

(39

48)

Rev

enu

ep

erfa

rm(1

000

0K

RW

)3

286

(54

11)

529

0(6

788

)6

363

(54

34)

524

1(6

157

)N

etin

com

ep

erfa

rm(1

00

00K

RW

)2

066

(40

79)

217

6(4

612

)1

947

(37

85)

207

6(4

220

)

Cate

gori

cal

vari

able

sF

requ

ency

(w

ith

inea

chgr

oup

)E

du

cati

onP

rim

ary

school

13(2

95

)26

(26

0)

27(3

65

)66

(30

3)

Sec

on

dary

sch

ool

10(2

27

)38

(38

0)

22(2

97

)70

(32

1)

Hig

hsc

hool

15(3

41

)31

(31

0)

17(2

30

)63

(28

9)

Un

iver

sity

6(1

36

)5

(50

)

8(1

08

)

19(8

7

)

aNumber

ofcrops=

1or2

bNumber

ofcrops=

3or4

cNumber

ofcropsge

5d10000KRW

=853USD

in30th

July

2015

9

minus2 minus1 0 1 2

minus2

0minus

10

00

05

10

PC 1 (31 explained variance)

PC

2 (

189

e

xpla

ined

var

ianc

e)

Education

Age

Farming experience

Farm size (ha)

Number of crops

Subsidy (per ha)

Net income

1minus2 crops3minus4 cropsgt 4 crops

Figure 1 Principal Component Analysis of farmersrsquo characteristics Arrows show original variables Thedirection and the length of the arrows show the correlation between the original variables and the principalcomponents The more an arrow is parallel to the axis the more the original variable is related to thisparticular principal component

Table 2 Loadings from PCA

PC 1 PC 2 PC 3 PC 4 PC 5

Education 0564 0130Age ndash0534 ndash0237 0119 ndash0136 0248Farming experience ndash0569 ndash0218Farm size (ha) 0700 ndash0611Number of crops 0499 ndash0601 0151 0597Subsidy (per ha) 0154 ndash0273 ndash0653 ndash0636 ndash0249Net income 0181 0348 0445 ndash0708 0356

10

Table 3 Number of farmers cultivating the eight main crops in the watershed of the Soyang Lake in theGangwon Province

Rank Crop Number of farmers

1 Pepper 1332 Potato 1163 Beans 904 Ligularia fischeri 645 Rice 596 Radish 527 Cabbage 427 Maize 42

as they were the majorities in each group Then we looked at the most selected crops by eachgroup of farmers Rice was the most frequently cultivated crop by farmers who cultivated asingle crop However as rice is the main staple grain in South Korea rice is highly subsidisedby the government (Korea Rural Economic Institute 2015) which might lead to differentprice conditions compared to the other single crops Therefore we decided not to have riceas a representative crop for the single crop farming but compared all six chosen crops Inthe second group 50 farmers grew three crops most frequently beans pepper and cabbageFinally in the last group among the 25 farmers with five crops potato pepper beanscabbage and Ligularia fischeri dominated However because Ligularia fischeri was relativelynewly introduced to consumers the price data contained large and regularly occurring gaps(Supplementary Table ST1) Therefore SSA could not be carried out for this crop As analternative we have included radish in the five-crop portfolio as the sixth most frequentlychosen crop by farmers who grew five crops We calculated the relative proportions of thesethree or five main crops and composed the empirical crop portfolios as follows

(1) Single crop farming six major crops (100)

(2) Three-crop portfolio beans (350) pepper (325) and cabbage (325)

(3) Five-crop portfolio potato (290) pepper (277) beans (174) cabbage (144)and radish (115)

32 Crop price fluctuations

321 Single crops

Figure 2 shows the variabilities of crop price fluctuations among six main crops in theGangwon Province of South Korea The visual comparison of price data showed that the riceprice was extremely stable compared to any other analysed crops during the study period(Figure 2 and Supplementary Figure SF3 for non-normalised price data) Because rice is themost important cereal crop in South Korea (Korea Rural Economic Institute 2015) severalpolicy instruments such as government buffer stock schemes and direct payments were usedto stabilise the rice price (Park et al 2010) Even though the price for beans was alsorelatively stable a sharp increase was registered in 2004 The price for beans in South Koreais highly dependent on foreign trade and is directly influenced by the global market (OECD

11

Year

Nor

mal

ized

pric

e (K

RW

kg)

minus40

000

2000

6000

1996 1998 2000 2002 2004 2006 2008 2010 2012

ricebeans

potatoradisch

cabbagepepper

Ligularia fischeri

Year

Nor

mal

ized

yie

ld (

ton

ha)

minus15

minus10

minus5

05

1015

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

rice beans potato radisch cabbage pepper

Figure 2 The variability of the normalised crop price (left) and the normalised yield (right) over the analysedperiod The respective mean was subtracted from each time series

2008) Because the US soybean crop yield in 2003 has been the lowest since 1992 theprice in 2004 increased dramatically (USDA 2007) Similarly a large price rise for cabbagewas observed in 2010 although for a different reason (Supplementary Figure SF3 (e) andFigure 2) Due to bad weather in 2010 the supply of cabbage did not meet the demand(Kwon 2012) In comparison to rice and beans the prices for pepper and Ligularia fischerifluctuated strongly

Figure 3 shows the results of the SSA decomposition of the crop prices We consideredfour time scales of fluctuations and evaluated their importance by the ratio of the eigenvalues(cf numbers in parenthesis in Figure 3) These numbers show how much each time scalecontributes to the reconstruction of the original time series We associate the periodicitiesof 24 months and more with a trend and those of 6ndash24 months with seasonal fluctuationsThe third (3ndash59 months) and the fourth (lt 29 months) time scales are however too shortto be interpreted

The prices for rice and beans showed a large contribution of the trend (701 and 546respectively) and a minor one on the smallest time scale (26 and 4 respectively) Thisconfirms the visual impression of stability in Figure 2 Except for rice the crop price datashowed considerable seasonal patterns with the ratio of eigenvalues exceeding 30 Radishand pepper exhibited an especially strong seasonal fluctuation namely 436 and 426respectively Compared to rice and beans cabbage and pepper had a substantial contributionto fluctuations at the smallest time scale (124 and 175 respectively)

322 Crop portfolios

The thee-crop portfolio consisted of beans (35) pepper (325) and cabbage (325)(Figure 4 (a)) The SSA of single crops (Figure 3) showed that the bean price was one ofthe least fluctuating and dominated by the trend whilst pepper and cabbage exhibited alarge seasonal variation The combination of them increased the contribution of the trend(compared to pepper) and decreased the importance of seasonal fluctuations (compared topepper and cabbage) (Figure 4 (a)) However in comparison to the trend-dominated beanprice the fluctuations on all but the largest time scale (trend) increased

The five-crop portfolio included potato (29) pepper (277) beans (174) cabbage(144) and radish (115) (Figure 4 (b)) Compared to the trend-dominated bean price

12

1600

1800

2000

original data gt 24 months (701)(a)

Time

minus50

50

6minus24 months (183)

Time

minus20

20

3minus59 months (89)

Time

minus10

515lt 29 months (26)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

5000

8000

original data gt 24 months (546)(b)

Time

minus20

0020

006minus24 months (303)

Time

minus20

040

0

3minus59 months (111)

Time

minus20

00

200

lt 29 months (4)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

050

015

0025

00

original data gt 24 months (314)(c)

Time

minus40

040

06minus24 months (357)

Time

minus30

030

0 3minus59 months (237)

Time

minus10

020

0lt 29 months (92)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500 original data gt 24 months (238)(d)

Time

minus20

040

06minus24 months (436)

Time

minus20

020

0 3minus59 months (232)

Time

minus10

010

0lt 29 months (95)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500

original data gt 24 months (252)(e)

Time

minus50

050

0

6minus24 months (39)

Time

minus20

020

0 3minus59 months (234)

Time

minus20

020

0

lt 29 months (124)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

6000

1200

0 original data gt 24 months (122)(f)

Time

minus40

0040

006minus24 months (426)

Time

minus20

0020

00 3minus59 months (277)

Time

minus20

0020

00lt 29 months (175)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 3 SSA decomposition of the crop prices (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper Four groups of fluctuation were considered larger than 24 months (trend) 6ndash24 months (sea-sonality) 3ndash59 months smaller than 29 months The number in parenthesis shows the ratio of eigenvaluesThe trend component contains the mean the others show the variability around it

13

1000

3000

5000

original data gt 24 months (239)(a)

Time

minus20

0020

006minus24 months (352)

Time

minus50

050

0 3minus59 months (259)

Timeminus

400

400lt 29 months (15)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

1000

3000

5000

original data gt 24 months (204)(b)

Time

minus20

0020

006minus24 months (408)

Time

minus50

050

0 3minus59 months (236)

Time

minus40

040

0lt 29 months (152)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 4 SSA decomposition of the portfolio prices (a) three-crops portfolio (beans (350) pepper (325)and cabbage (325)) and (b) five-crops portfolio (potato (29) pepper (277) beans (174) cabbage(144) and radish (115))For both portfolio four periods of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it

the contribution of the trend decreased from 546 to 204 Additionally the contributionof the seasonal fluctuation remained comparable to the other crops that have a strong sea-sonal pattern In summary the results of SSA decomposition were similar to the portfoliocomposed of three crops Indeed the summed contributions of the larger time scales (trendand seasonality) as well as those on the smaller time scales differed only slightly

33 Crop yield fluctuations

An in-depth analysis of seasonality was not possible because the time series of yieldconsisted of annual measurements Therefore we only extracted the trend and calculatedthe dominant frequency of the remaining periodicities (Figure 5) The result of SSA showedthat the contribution of the trend varied from 333 to 665 Accordingly the importanceof periodicities ranged from 335 to 667 Their dominant frequency covered 25 years to107 years

In general crop yield had an upwards trend during the analysed period except forradish and cabbage (Figure 5) Four of the six analysed crops namely rice beans potatoand pepper showed increasing trends in the yields In contrast the yield of radish andcabbage had decreased during the 23-year analysed period There were more negative thanpositive extreme values outside the range of the standard deviation of the trend Additionallythe amplitude of negative values was often larger than that of positive values (Figure 5)Interestingly large negative values occurred in different years for different crops In 1980and 1993 for example the rice yield decreased sharply whereas there was a relatively high

14

23

45

6

original data trend (457)(a)

Time

minus2

01

2

25 years (543)

1965 1975 1985 1995 2005

Yie

ld (

ton

ha)

Year

10

12

14

16

18

20

original data trend (333)(b)

Time

minus0

30

00

3

4 years (667)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

1015

2025

3035

40 original data trend (424)(c)

Time

minus10

0527 years (576)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3034

3842 original data trend (349)

(d)

Time

minus6

04

8

46 years (651)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3540

4550

5560 original data trend (344)

(e)

Time

minus10

0523 years (656)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

24

68

1012 original data trend (665)

(f)

Time

minus3

minus1

13

107 years (335)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

Figure 5 SSA decomposition of the crop yield (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper The number in parenthesis shows the ratio of eigenvalues The trend component contains themean the others show the variability around it The yellow area shows plusmn standard deviation around thetrend component Note that the time scale is years and not months as for the price data Fluctuations withperiods of 23 years and 16 years (trend) were chosen for rice and the other crops respectively

15

Year

Rea

l Rev

enue

(M

illio

n K

RW

haminus1

year

minus1)

020

4060

1996 1998 2000 2002 2004 2006 2008 2010

ricebeans

potatoradisch

cabbagepepper

threeminuscrop portfoliofiveminuscrop portfolio

Figure 6 Real revenue for single crops and the empirical crop portfolios

yield in potato in the same year In 1996 the radish yield was very low and the rice yieldmoderately high (See Figure 5 and Supplementary Figure SF4)

The sharp drops of yield often followed damages caused by unusual weather eventsEspecially in 1980 the rice yield reached only 587 of the target yield of South Koreadue to low temperature (Park et al 2010) In 1987 and 2010 radish and cabbage werealso influenced by bad weather (Kwon 2012) Frequent rain and lack of sunlight duringseeding period harmed stabilising seeds (Han and Kim 2010) In addition the yield ofradish and cabbage has declined as the consumption decreases and imports increase (KoreaRural Economic Institute 2015) Actually the import of cabbage has increased since 2003and westernised eating habits of South Koreans has decreased its consumption by 2 peryear since 2002 (Korea Rural Economic Institute 2015)

34 Risk adjusted revenue

The revenue and the Sharpe ratio for each crop portfolio are depicted in Figure 6 andTable 4 The Sharpe ratio is often used to assess the portfolio performance (Blank 1990Roche and McQuinn 2004 Gaydon et al 2012) For example Roche and McQuinn (2004)calculated the Sharpe ratio for the farm land allocation portfolio for grains and Gaydon et al(2012) used it for comparing water management options and their contribution to the farmincome

Figure 6 shows the temporal change of the real revenue of single crops and three-and five-crop portfolios Large differences between the six main crops were observed Rice and beansshowed a stable but the smallest and decreasing revenue compared to the other crops overthe analysed period Pepper showed the highest revenue with the highest standard deviation(Table 4) In the portfolio the mean revenue doubled or tripled and the standard deviationincreased with the number of crops compared to rice and bean single crop farming Althoughthe mean revenue of the crop portfolios was smaller compared to potato and pepper itsstandard deviation decreased The difference between the three- and the five-crop portfoliosin mean and standard deviation was only minor

16

Table 4 Risks adjusted revenue for the analysed period from 1996 to 2011

Crop selection Mean (million KRW) SD Sharpe ratio

Single croprice 1085 173 627

beans 596 175 340potato 3092 770 401radish 1476 298 495

cabbage 2288 435 526pepper 3294 1420 232

three-crop portfolio 2023 532 380five-crop portfolio 2412 560 430

4 Discussion

An advantage of decomposing the time series is that we can not only identify the mostfluctuating crop over time but also quantify different components of fluctuations in eachcrop Fluctuations on larger time scales (trend and seasonality) are easier for farmers toface than short-time variations which are more difficult to address in the planning processIn order to distinguish four time scales of fluctuations in each crop selection we calculatedthe ratio of eigenvalue for each time scale The ratio of eigenvalue stands for the quality ofthe reconstruction of the original time series by a certain component The larger this ratiothe more important the component will be for the reconstruction Among four time scalesthe first and the second scales can be interpreted as trend and seasonality respectively thethird and the fourth scales however were too short to be identified

Farmersrsquo decision on which crop to grow how to allocate the land to grow multiple cropsand when to harvest and sell them plays a crucial role to secure their revenue (Fafchamps1992 Kantanantha et al 2010 Klasen et al 2013) Our result showed that each crop had adifferent fluctuation pattern that highly influenced the farm revenue depending on farmersrsquocrop selection The sum of the first two ratios of eigenvalues for crop price ranged from 548(pepper) to 884 (rice) The larger the contribution of trend and seasonality the less short-time variability is contained in the data Four of the six analysed crops contained notableseasonal patterns The SSA of the three- and the five-crop portfolios also revealed thatimportant seasonal variation still remained in the monthly price data Therefore seasonalityprobably has an important impact on farmersrsquo decisions regarding the times for harvestingor marketing of their crops

The risk adjusted revenue calculated with the Sharpe ratio allows us to compare how muchrevenue standardised per 1 of revenue can be guaranteed for farmers in each crop selectionThe combination of these methods provides more information to support farmersrsquo decision oncrop selection Although the results of SSA and the Sharpe ratio showed that rice and beanfarming were the most stable they provided the lowest revenue The revenue of the three-and the five-crop portfolios was more than two times larger than in rice farming howeverat the same time the standard deviation tripled (Table 4) It indicates that the diversified

17

Time

Pric

e (U

SDto

n)

500

1000

1500

2000

1996 1998 2000 2002 2004 2006 2008 2010 2012

Korean domestic rice price World rice price

200

600

1000 original data gt 24 months (684)

Time

minus10

050

6minus24 months (154)

Time

minus10

00

100

3minus59 months (107)

Time

minus40

040

lt 29 months (54)

1991 1997 2003 2009 2015

Pric

e (U

SD

ton)

Year

Figure 7 Korean domestic rice price converted in USDton and world rice price in USDton (left) SSAdecomposition of the world rice price (right) Four groups of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it The world rice data was Thailand nominal price quote obtained from the World BankGlobal Economic Monitor (GEM) Commodities The exchange rate from Korean Won to USD for each yearwas obtained from the World Bank World Development Indicators

farming could support larger revenue This is in accordance with the study by Bhattacharyya(2008) who showed that a rice dominated farming system in India was changed to high-valuecrops for larger revenue Furthermore an analysis in Argentina showed that diversifiedfarming increased the mean return on capital with a lower coefficient of variation (Pacın andOesterheld 2014) Hence the multiple crop farming may be a means of enhancing revenue(Ali et al 2004 Winters et al 2006 Pacın and Oesterheld 2014 Rahman and Kazal 2015)However the diversification took place slowly due to agricultural subsidies concentrated ona certain crop such as rice in India (Bhattacharyya 2008) This might also be the case inSouth Korea

To examine the artificial stability of the rice price in South Korea we compared thedomestic rice price with the world rice price in USD (Figure 7) As the exchange rate variesbetween years the domestic rice price converted in USD fluctuated more compared to theone in KRW We refer to the SSA result of the rice price in KRW to keep consistency unlessmentioned While the world rice price increased drastically in 2008 as a result of the oilcrisis (Figure 7 right) the Korean domestic price was not affected by it and remained stable(Figure 3 (a)) Overall rice price in the global market fluctuates more than in the SouthKorean domestic market (Baffes and Cosic 2013) Furthermore the Korean domestic priceis more than double or triple the world price ndash the result of a substantial governmentalsupport (Figure 7 left)

South Korea used to have a higher protection for domestic rice farming mainly throughtariff and non-tariff barriers in comparison to other OECD countries (Aksoy 2005) Amongother conventional crops Korean subsidy policy focuses particularly on rice farming by sup-

18

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

explain Thus the first principal component explains the largest proportion of variance inthe data set

After analysing the socio-economic condition of farmers we clustered the data by thenumber of crops chosen per farm household to understand how farmers construct their port-folios of crops Farmers were categorised into three groups according to the number of cropsThe most frequently chosen crops within each group were used to construct empirical cropportfolios For instance to determine the crop portfolio for three crops the major cropschosen by the group of farmers who cultivated three or four crops were considered Basedon these categories three empirical crop portfolios were constructed

Subsequently we compared temporal fluctuations of the crop price and yield betweensingle crops and the empirical portfolios In order to detect fluctuations of crop price andyield we analysed nation-wide statistical data (Table ST1 in the online SupplementaryMaterial) The crop price data was provided by the Korea Agro-Fisheries amp Food TradeCorporation (KAMIS) and the Ministry of Food Agriculture Forestry and Fisheries Formost of the analysed crops the monthly price data was available from 1996 to 2011 Annualcrop yield data of the Gangwon Province (mostly 1980 to 2011) was obtained from the cropproduction survey by Korean Statistical Information System (KOSIS) The yield data forLigularia fischeri2 was not available

23 Risk adjusted revenue

The calculation of risk adjusted revenue is motivated by the Sharpe ratio (Sharpe 1994)a measure of risk-adjusted performance of mutual funds We first calculated the nominalrevenue by multiplying the annual yield by the annual mean price of crops Then thenominal revenue was adjusted by the Consumer Price Index (CPI) to get the real revenuewith 2010 being the reference year The CPI for living necessaries were obtained from KOSISSubsequently the Sharpe ratio was calculated as

θp =microp minusRf

σp (1)

where microp is the average performance of the portfolio (ie the mean real revenue see below)Rf is the risk-free rate and σp is the standard deviation of the portfolio We used the Sharperatio to compare investment options to identify which empirical crop portfolio offered themost risk-efficient investment (Elton et al 2007) The higher the Sharpe ratio the lowerthe investment risk in an empirical crop portfolio

In this study we assume that the average performance is only based on the farm revenuewhich is the income that a farmer gains from only actual farming activities off-farm incomeand direct government subsidies were not included We omitted the risk-free rate because itwas the same for all empirical crop portfolios Under these assumptions the risk adjustedrevenue equals the mean real revenue over the period 1996 to 2011 divided by its standarddeviation

2Ligularia fischeri is one of the most popular edible wild plants in South Korea cultivated in mountainousregions like the Gangwon Province It inhabits mostly central and eastern Asia (Brickell 2008)

5

24 Singular Spectrum Analysis

The Singular Spectrum Analysis (SSA) is a method for time series analysis and forecast-ing Since its introduction by Broomhead and King (1986ab) different SSA methodologieshave been developed (eg Golyandina and Zhigljavsky 2013) In this work we use SSA inits basic form (Basic SSA) or repeatedly (Sequential SSA)

Basic SSA is a non-parametric and model-free technique that decomposes a time seriesinto a set of time series such as trend (modulated) periodicities and noise Here we definetrend as any slowly varying time series Thus the main goal of SSA decomposition isobtaining components of the original time series that can be interpreted more easily In thissense Basic SSA can be regarded as a global data-driven frequency decomposition The onlyassumption behind Basic SSA is that the original time series can be represented by a sumof different components (Golyandina and Zhigljavsky 2013) Therefore it can be applied toany time series regardless of its stationarity

We first describe briefly the algorithm of Basic SSA closely following Golyandina andZhigljavsky (2013) and then explain Sequential SSA Basic SSA consists of time series de-composition and reconstruction

Decomposition Consider a real-valued time series XN = (x1 xN) where N is the numberof data points First it is converted into a LtimesK trajectory matrix X

X =

x1 x2 x3 xKx2 x3 x4 xK+1

x3 x4 x5 xK+2

xL xL+1 xL+2 xN

(2)

Its columns consist of lagged vectors of length L of the original time series In other wordsthe trajectory matrix is constructed by moving a window of length L through the time seriesand collecting all K = N minus L+ 1 segments

The second step is the Singular Value Decomposition (SVD) of this trajectory matrix

X = UΛVT (3)

where U and V are the left and right singular vectors respectively and Λ contains d positivesingular values

radicλ1 ge middot middot middot ge

radicλd gt 0 Note that the singular values of X are the square

roots of the eigenvalues of the matrix XXT The collections (radicλi Ui Vi) i = 1 d of

related singular values and singular vectors are called eigentriples

Reconstruction To reconstruct components of the time series we first have to identify whicheigentriples should be grouped together The aim of grouping is to identify the additivecomponents of the time series We partition the set of indices 1 d into m disjointssubsets I1 Im and reconstruct the component time series

XIp =sumiisinIp

radicλiUiV

Ti p = 1 m (4)

6

Thus we obtain the decomposition of the original trajectory matrix

X = XI1 + middot middot middot+ XIm (5)

To recover the additive components of the original time series we have to convert the trajec-tory matrices back to time series by averaging along the secondary diagonals of the matricesXIp

The quality of reconstruction is measured by the ratio of eigenvalues The larger theeigenvalue λi the larger is its ratio λi

sumi λi and the more important is the component for

the reconstruction of the original time series In order for this ratio to be meaningful thetime series should be normalised by subtracting the mean before the SSA (Golyandina andZhigljavsky 2013)

The window length L is a crucial parameter in SSA that strongly influences the decom-position An inappropriate choice of L might lead to separability issues The reconstructedcomponents contain a mixture of different periodicities or periodicities and trend Conse-quently the interpretation of such components is difficult There is no universal rule forchoosing L however some general recommendations exist Usually L le N2 is chosen andmore details can be extracted for larger L If a dominant periodicity T is present (like theyearly cycle) LT should be an integer For small L SSA is equivalent to smoothing witha linear filter of width 2L minus 1 (Golyandina and Zhigljavsky 2013) We chose L = 5 todecompose the short yield time series

The longer price time series showed a complex trend and periodicities For such timeseries the choice of L might become difficult Indeed choosing a large L could mix upperiodicities and trend in the same component On the contrary for a small L periodiccomponents might be inseparable from each other To avoid these separability issues wedecomposed the price time series by Sequential SSA ndash a reiteration of Basic SSA First thetrend is extracted with a small L1 and removed from the original time series Subsequentlythe periodicities are extracted from the residual time series with a larger L2 (Golyandina andZhigljavsky 2013) We chose L1 = 12 and L2 = 48 to extract the trend and the periodicitiesrespectively

Our goal is to compare fluctuations between single crops and crop portfolios It is in-tuitively clear that with respect to revenue stability fluctuations with shorter periods aremore problematic than those with larger periods Therefore we compared the time serieson different time scales For the price data we considered four groups of fluctuations fluc-tuations with periods larger than 24 months (trend) periods of 6ndash24 months (seasonality)3ndash59 months and smaller than 29 months However for the yield data we only distinguishedbetween the trend and the remaining periodicities because the time series were short andconsisted of yearly measurements Different periods for rice and the other crops were chosenas the length of the data was different fluctuations with periods of 23 years and 16 years(trend) for rice and the other crops respectively From now on trend and seasonality willtake on these temporal meanings In the reconstruction step (see above) we grouped theeigentriples according to the dominant periodicity that we calculated from the periodogramof the components A similar approach was used by Mahecha et al (2010) for example tocompare observations with simulated data in biospherendashatmosphere modelling The impor-tance of the fluctuations at a certain time scale is shown by the ratio of the eigenvalues

7

We decomposed the price and the yield of single crops and the price of the crop portfoliosby SSA Because the revenue time series contained only 16 values they were too short foran analysis by SSA All calculations were done in R (R Core Team 2013) using the packageRssa (Korobeynikov 2010 Golyandina and Korobeynikov 2013)

3 Results

31 Farmersrsquo crop selection and empirical crop portfolios

We classified the 218 farmers into three groups based on the number of cultivated cropsGroup 1 included farmers who cultivated one or two crops (n = 44) group 2 those with threeor four crops (n = 100) and group 3 summarised farmers cultivating more than five crops(n = 74) These three groups became the basis of the empirical crop portfolios

The mean age in each group of farmers was 55 54 and 53 for group 1 group 2 and group3 respectively (Table 1) The farming experience increased with the increasing number ofcrops cultivated In group 1 the farm size was smaller compared to the other two groupsThe farm costs (costs of rent labour fertiliser and others) increased with increasing numberof crops which led to lower net income for group 3 with a higher standard deviation Thelevel of education was available as a categorical variable The farmers in group 2 had highereducation compared to the other two groups Note that the total number of farmers in eachgroup was different Among those who had university education 42 of farmers cultivatedmore than five crops

The results of PCA are summarised in Figure 1 and Table 2 The first two principalcomponents (PC) explained approximately 50 of the variance (Supplementary Figure SF6)The first component accounted for 31 of the variance and was positively correlated witheducation and negatively correlated with farming experience The second component ex-plained 189 of the variance and was mainly related to the farm size and the number ofcrops Subsidy was negatively related to PC 2 and had thus an opposite effect comparedto the farm size and the number of crops In other words PC 1 distinguished farmers withmore education and less farming experience from those with less education and more farmingexperience as the main source of variability in the socio-economic background of farmers PC2 contrasted farmers with large farms growing many crops and having less subsidies to thosewith smaller farms and less grown crops having larger subsidies The additional informationregarding the farming management type (eg organic farming partially converted farmingand conventional farming) is supplied in the Supplementary Figure SF2

In total 83 types of crops were cultivated in the watershed of the Soyang Lake in theGangwon Province However 93 of the farmers cultivated one or more crops out of theseven main ones (Table 3) Maize and cabbage shared the same rank However becausemaize is one of the forage crops in South Korea the market conditions differ from othercrops and we excluded it from further analysis Note that in the survey farmers recorded allcrops they planted Therefore the total number of crops and the total number of farmersdiffer

The most critical part of building the empirical crop portfolios was to choose the crops andto decide on their relative contribution In each group of farmers we have selected those whocultivated the smallest number of crops namely one three and five The single crop farmingwas the basis for the comparison Subsequently three- and five-crop portfolios were chosen

8

Tab

le1

Des

crip

tive

stati

stic

sof

farm

ersrsquo

chara

cter

isti

csin

each

gro

up

Gro

up

1a

Gro

up

2b

Gro

up

3c

Tota

l

Conti

nu

ou

sva

riab

les

Aver

age

(sta

nd

ard

dev

iati

on)

Age

(yea

rs)

552

(10

5)54

2(9

8)

539

(82

)54

3(9

4)

Far

min

gex

per

ien

ce(y

ears

)26

6(1

32)

279

(13

2)29

9(1

38)

283

(13

4)F

arm

Siz

e(h

a)2

2(3

3)

31

(32

)3

8(3

9)

32

(35

)T

otal

Cos

tp

erfa

rm(1

00

00

KR

Wd)

121

9(1

691

)3

114

(33

94)

441

5(5

019

)3

165

(39

48)

Rev

enu

ep

erfa

rm(1

000

0K

RW

)3

286

(54

11)

529

0(6

788

)6

363

(54

34)

524

1(6

157

)N

etin

com

ep

erfa

rm(1

00

00K

RW

)2

066

(40

79)

217

6(4

612

)1

947

(37

85)

207

6(4

220

)

Cate

gori

cal

vari

able

sF

requ

ency

(w

ith

inea

chgr

oup

)E

du

cati

onP

rim

ary

school

13(2

95

)26

(26

0)

27(3

65

)66

(30

3)

Sec

on

dary

sch

ool

10(2

27

)38

(38

0)

22(2

97

)70

(32

1)

Hig

hsc

hool

15(3

41

)31

(31

0)

17(2

30

)63

(28

9)

Un

iver

sity

6(1

36

)5

(50

)

8(1

08

)

19(8

7

)

aNumber

ofcrops=

1or2

bNumber

ofcrops=

3or4

cNumber

ofcropsge

5d10000KRW

=853USD

in30th

July

2015

9

minus2 minus1 0 1 2

minus2

0minus

10

00

05

10

PC 1 (31 explained variance)

PC

2 (

189

e

xpla

ined

var

ianc

e)

Education

Age

Farming experience

Farm size (ha)

Number of crops

Subsidy (per ha)

Net income

1minus2 crops3minus4 cropsgt 4 crops

Figure 1 Principal Component Analysis of farmersrsquo characteristics Arrows show original variables Thedirection and the length of the arrows show the correlation between the original variables and the principalcomponents The more an arrow is parallel to the axis the more the original variable is related to thisparticular principal component

Table 2 Loadings from PCA

PC 1 PC 2 PC 3 PC 4 PC 5

Education 0564 0130Age ndash0534 ndash0237 0119 ndash0136 0248Farming experience ndash0569 ndash0218Farm size (ha) 0700 ndash0611Number of crops 0499 ndash0601 0151 0597Subsidy (per ha) 0154 ndash0273 ndash0653 ndash0636 ndash0249Net income 0181 0348 0445 ndash0708 0356

10

Table 3 Number of farmers cultivating the eight main crops in the watershed of the Soyang Lake in theGangwon Province

Rank Crop Number of farmers

1 Pepper 1332 Potato 1163 Beans 904 Ligularia fischeri 645 Rice 596 Radish 527 Cabbage 427 Maize 42

as they were the majorities in each group Then we looked at the most selected crops by eachgroup of farmers Rice was the most frequently cultivated crop by farmers who cultivated asingle crop However as rice is the main staple grain in South Korea rice is highly subsidisedby the government (Korea Rural Economic Institute 2015) which might lead to differentprice conditions compared to the other single crops Therefore we decided not to have riceas a representative crop for the single crop farming but compared all six chosen crops Inthe second group 50 farmers grew three crops most frequently beans pepper and cabbageFinally in the last group among the 25 farmers with five crops potato pepper beanscabbage and Ligularia fischeri dominated However because Ligularia fischeri was relativelynewly introduced to consumers the price data contained large and regularly occurring gaps(Supplementary Table ST1) Therefore SSA could not be carried out for this crop As analternative we have included radish in the five-crop portfolio as the sixth most frequentlychosen crop by farmers who grew five crops We calculated the relative proportions of thesethree or five main crops and composed the empirical crop portfolios as follows

(1) Single crop farming six major crops (100)

(2) Three-crop portfolio beans (350) pepper (325) and cabbage (325)

(3) Five-crop portfolio potato (290) pepper (277) beans (174) cabbage (144)and radish (115)

32 Crop price fluctuations

321 Single crops

Figure 2 shows the variabilities of crop price fluctuations among six main crops in theGangwon Province of South Korea The visual comparison of price data showed that the riceprice was extremely stable compared to any other analysed crops during the study period(Figure 2 and Supplementary Figure SF3 for non-normalised price data) Because rice is themost important cereal crop in South Korea (Korea Rural Economic Institute 2015) severalpolicy instruments such as government buffer stock schemes and direct payments were usedto stabilise the rice price (Park et al 2010) Even though the price for beans was alsorelatively stable a sharp increase was registered in 2004 The price for beans in South Koreais highly dependent on foreign trade and is directly influenced by the global market (OECD

11

Year

Nor

mal

ized

pric

e (K

RW

kg)

minus40

000

2000

6000

1996 1998 2000 2002 2004 2006 2008 2010 2012

ricebeans

potatoradisch

cabbagepepper

Ligularia fischeri

Year

Nor

mal

ized

yie

ld (

ton

ha)

minus15

minus10

minus5

05

1015

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

rice beans potato radisch cabbage pepper

Figure 2 The variability of the normalised crop price (left) and the normalised yield (right) over the analysedperiod The respective mean was subtracted from each time series

2008) Because the US soybean crop yield in 2003 has been the lowest since 1992 theprice in 2004 increased dramatically (USDA 2007) Similarly a large price rise for cabbagewas observed in 2010 although for a different reason (Supplementary Figure SF3 (e) andFigure 2) Due to bad weather in 2010 the supply of cabbage did not meet the demand(Kwon 2012) In comparison to rice and beans the prices for pepper and Ligularia fischerifluctuated strongly

Figure 3 shows the results of the SSA decomposition of the crop prices We consideredfour time scales of fluctuations and evaluated their importance by the ratio of the eigenvalues(cf numbers in parenthesis in Figure 3) These numbers show how much each time scalecontributes to the reconstruction of the original time series We associate the periodicitiesof 24 months and more with a trend and those of 6ndash24 months with seasonal fluctuationsThe third (3ndash59 months) and the fourth (lt 29 months) time scales are however too shortto be interpreted

The prices for rice and beans showed a large contribution of the trend (701 and 546respectively) and a minor one on the smallest time scale (26 and 4 respectively) Thisconfirms the visual impression of stability in Figure 2 Except for rice the crop price datashowed considerable seasonal patterns with the ratio of eigenvalues exceeding 30 Radishand pepper exhibited an especially strong seasonal fluctuation namely 436 and 426respectively Compared to rice and beans cabbage and pepper had a substantial contributionto fluctuations at the smallest time scale (124 and 175 respectively)

322 Crop portfolios

The thee-crop portfolio consisted of beans (35) pepper (325) and cabbage (325)(Figure 4 (a)) The SSA of single crops (Figure 3) showed that the bean price was one ofthe least fluctuating and dominated by the trend whilst pepper and cabbage exhibited alarge seasonal variation The combination of them increased the contribution of the trend(compared to pepper) and decreased the importance of seasonal fluctuations (compared topepper and cabbage) (Figure 4 (a)) However in comparison to the trend-dominated beanprice the fluctuations on all but the largest time scale (trend) increased

The five-crop portfolio included potato (29) pepper (277) beans (174) cabbage(144) and radish (115) (Figure 4 (b)) Compared to the trend-dominated bean price

12

1600

1800

2000

original data gt 24 months (701)(a)

Time

minus50

50

6minus24 months (183)

Time

minus20

20

3minus59 months (89)

Time

minus10

515lt 29 months (26)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

5000

8000

original data gt 24 months (546)(b)

Time

minus20

0020

006minus24 months (303)

Time

minus20

040

0

3minus59 months (111)

Time

minus20

00

200

lt 29 months (4)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

050

015

0025

00

original data gt 24 months (314)(c)

Time

minus40

040

06minus24 months (357)

Time

minus30

030

0 3minus59 months (237)

Time

minus10

020

0lt 29 months (92)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500 original data gt 24 months (238)(d)

Time

minus20

040

06minus24 months (436)

Time

minus20

020

0 3minus59 months (232)

Time

minus10

010

0lt 29 months (95)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500

original data gt 24 months (252)(e)

Time

minus50

050

0

6minus24 months (39)

Time

minus20

020

0 3minus59 months (234)

Time

minus20

020

0

lt 29 months (124)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

6000

1200

0 original data gt 24 months (122)(f)

Time

minus40

0040

006minus24 months (426)

Time

minus20

0020

00 3minus59 months (277)

Time

minus20

0020

00lt 29 months (175)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 3 SSA decomposition of the crop prices (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper Four groups of fluctuation were considered larger than 24 months (trend) 6ndash24 months (sea-sonality) 3ndash59 months smaller than 29 months The number in parenthesis shows the ratio of eigenvaluesThe trend component contains the mean the others show the variability around it

13

1000

3000

5000

original data gt 24 months (239)(a)

Time

minus20

0020

006minus24 months (352)

Time

minus50

050

0 3minus59 months (259)

Timeminus

400

400lt 29 months (15)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

1000

3000

5000

original data gt 24 months (204)(b)

Time

minus20

0020

006minus24 months (408)

Time

minus50

050

0 3minus59 months (236)

Time

minus40

040

0lt 29 months (152)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 4 SSA decomposition of the portfolio prices (a) three-crops portfolio (beans (350) pepper (325)and cabbage (325)) and (b) five-crops portfolio (potato (29) pepper (277) beans (174) cabbage(144) and radish (115))For both portfolio four periods of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it

the contribution of the trend decreased from 546 to 204 Additionally the contributionof the seasonal fluctuation remained comparable to the other crops that have a strong sea-sonal pattern In summary the results of SSA decomposition were similar to the portfoliocomposed of three crops Indeed the summed contributions of the larger time scales (trendand seasonality) as well as those on the smaller time scales differed only slightly

33 Crop yield fluctuations

An in-depth analysis of seasonality was not possible because the time series of yieldconsisted of annual measurements Therefore we only extracted the trend and calculatedthe dominant frequency of the remaining periodicities (Figure 5) The result of SSA showedthat the contribution of the trend varied from 333 to 665 Accordingly the importanceof periodicities ranged from 335 to 667 Their dominant frequency covered 25 years to107 years

In general crop yield had an upwards trend during the analysed period except forradish and cabbage (Figure 5) Four of the six analysed crops namely rice beans potatoand pepper showed increasing trends in the yields In contrast the yield of radish andcabbage had decreased during the 23-year analysed period There were more negative thanpositive extreme values outside the range of the standard deviation of the trend Additionallythe amplitude of negative values was often larger than that of positive values (Figure 5)Interestingly large negative values occurred in different years for different crops In 1980and 1993 for example the rice yield decreased sharply whereas there was a relatively high

14

23

45

6

original data trend (457)(a)

Time

minus2

01

2

25 years (543)

1965 1975 1985 1995 2005

Yie

ld (

ton

ha)

Year

10

12

14

16

18

20

original data trend (333)(b)

Time

minus0

30

00

3

4 years (667)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

1015

2025

3035

40 original data trend (424)(c)

Time

minus10

0527 years (576)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3034

3842 original data trend (349)

(d)

Time

minus6

04

8

46 years (651)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3540

4550

5560 original data trend (344)

(e)

Time

minus10

0523 years (656)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

24

68

1012 original data trend (665)

(f)

Time

minus3

minus1

13

107 years (335)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

Figure 5 SSA decomposition of the crop yield (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper The number in parenthesis shows the ratio of eigenvalues The trend component contains themean the others show the variability around it The yellow area shows plusmn standard deviation around thetrend component Note that the time scale is years and not months as for the price data Fluctuations withperiods of 23 years and 16 years (trend) were chosen for rice and the other crops respectively

15

Year

Rea

l Rev

enue

(M

illio

n K

RW

haminus1

year

minus1)

020

4060

1996 1998 2000 2002 2004 2006 2008 2010

ricebeans

potatoradisch

cabbagepepper

threeminuscrop portfoliofiveminuscrop portfolio

Figure 6 Real revenue for single crops and the empirical crop portfolios

yield in potato in the same year In 1996 the radish yield was very low and the rice yieldmoderately high (See Figure 5 and Supplementary Figure SF4)

The sharp drops of yield often followed damages caused by unusual weather eventsEspecially in 1980 the rice yield reached only 587 of the target yield of South Koreadue to low temperature (Park et al 2010) In 1987 and 2010 radish and cabbage werealso influenced by bad weather (Kwon 2012) Frequent rain and lack of sunlight duringseeding period harmed stabilising seeds (Han and Kim 2010) In addition the yield ofradish and cabbage has declined as the consumption decreases and imports increase (KoreaRural Economic Institute 2015) Actually the import of cabbage has increased since 2003and westernised eating habits of South Koreans has decreased its consumption by 2 peryear since 2002 (Korea Rural Economic Institute 2015)

34 Risk adjusted revenue

The revenue and the Sharpe ratio for each crop portfolio are depicted in Figure 6 andTable 4 The Sharpe ratio is often used to assess the portfolio performance (Blank 1990Roche and McQuinn 2004 Gaydon et al 2012) For example Roche and McQuinn (2004)calculated the Sharpe ratio for the farm land allocation portfolio for grains and Gaydon et al(2012) used it for comparing water management options and their contribution to the farmincome

Figure 6 shows the temporal change of the real revenue of single crops and three-and five-crop portfolios Large differences between the six main crops were observed Rice and beansshowed a stable but the smallest and decreasing revenue compared to the other crops overthe analysed period Pepper showed the highest revenue with the highest standard deviation(Table 4) In the portfolio the mean revenue doubled or tripled and the standard deviationincreased with the number of crops compared to rice and bean single crop farming Althoughthe mean revenue of the crop portfolios was smaller compared to potato and pepper itsstandard deviation decreased The difference between the three- and the five-crop portfoliosin mean and standard deviation was only minor

16

Table 4 Risks adjusted revenue for the analysed period from 1996 to 2011

Crop selection Mean (million KRW) SD Sharpe ratio

Single croprice 1085 173 627

beans 596 175 340potato 3092 770 401radish 1476 298 495

cabbage 2288 435 526pepper 3294 1420 232

three-crop portfolio 2023 532 380five-crop portfolio 2412 560 430

4 Discussion

An advantage of decomposing the time series is that we can not only identify the mostfluctuating crop over time but also quantify different components of fluctuations in eachcrop Fluctuations on larger time scales (trend and seasonality) are easier for farmers toface than short-time variations which are more difficult to address in the planning processIn order to distinguish four time scales of fluctuations in each crop selection we calculatedthe ratio of eigenvalue for each time scale The ratio of eigenvalue stands for the quality ofthe reconstruction of the original time series by a certain component The larger this ratiothe more important the component will be for the reconstruction Among four time scalesthe first and the second scales can be interpreted as trend and seasonality respectively thethird and the fourth scales however were too short to be identified

Farmersrsquo decision on which crop to grow how to allocate the land to grow multiple cropsand when to harvest and sell them plays a crucial role to secure their revenue (Fafchamps1992 Kantanantha et al 2010 Klasen et al 2013) Our result showed that each crop had adifferent fluctuation pattern that highly influenced the farm revenue depending on farmersrsquocrop selection The sum of the first two ratios of eigenvalues for crop price ranged from 548(pepper) to 884 (rice) The larger the contribution of trend and seasonality the less short-time variability is contained in the data Four of the six analysed crops contained notableseasonal patterns The SSA of the three- and the five-crop portfolios also revealed thatimportant seasonal variation still remained in the monthly price data Therefore seasonalityprobably has an important impact on farmersrsquo decisions regarding the times for harvestingor marketing of their crops

The risk adjusted revenue calculated with the Sharpe ratio allows us to compare how muchrevenue standardised per 1 of revenue can be guaranteed for farmers in each crop selectionThe combination of these methods provides more information to support farmersrsquo decision oncrop selection Although the results of SSA and the Sharpe ratio showed that rice and beanfarming were the most stable they provided the lowest revenue The revenue of the three-and the five-crop portfolios was more than two times larger than in rice farming howeverat the same time the standard deviation tripled (Table 4) It indicates that the diversified

17

Time

Pric

e (U

SDto

n)

500

1000

1500

2000

1996 1998 2000 2002 2004 2006 2008 2010 2012

Korean domestic rice price World rice price

200

600

1000 original data gt 24 months (684)

Time

minus10

050

6minus24 months (154)

Time

minus10

00

100

3minus59 months (107)

Time

minus40

040

lt 29 months (54)

1991 1997 2003 2009 2015

Pric

e (U

SD

ton)

Year

Figure 7 Korean domestic rice price converted in USDton and world rice price in USDton (left) SSAdecomposition of the world rice price (right) Four groups of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it The world rice data was Thailand nominal price quote obtained from the World BankGlobal Economic Monitor (GEM) Commodities The exchange rate from Korean Won to USD for each yearwas obtained from the World Bank World Development Indicators

farming could support larger revenue This is in accordance with the study by Bhattacharyya(2008) who showed that a rice dominated farming system in India was changed to high-valuecrops for larger revenue Furthermore an analysis in Argentina showed that diversifiedfarming increased the mean return on capital with a lower coefficient of variation (Pacın andOesterheld 2014) Hence the multiple crop farming may be a means of enhancing revenue(Ali et al 2004 Winters et al 2006 Pacın and Oesterheld 2014 Rahman and Kazal 2015)However the diversification took place slowly due to agricultural subsidies concentrated ona certain crop such as rice in India (Bhattacharyya 2008) This might also be the case inSouth Korea

To examine the artificial stability of the rice price in South Korea we compared thedomestic rice price with the world rice price in USD (Figure 7) As the exchange rate variesbetween years the domestic rice price converted in USD fluctuated more compared to theone in KRW We refer to the SSA result of the rice price in KRW to keep consistency unlessmentioned While the world rice price increased drastically in 2008 as a result of the oilcrisis (Figure 7 right) the Korean domestic price was not affected by it and remained stable(Figure 3 (a)) Overall rice price in the global market fluctuates more than in the SouthKorean domestic market (Baffes and Cosic 2013) Furthermore the Korean domestic priceis more than double or triple the world price ndash the result of a substantial governmentalsupport (Figure 7 left)

South Korea used to have a higher protection for domestic rice farming mainly throughtariff and non-tariff barriers in comparison to other OECD countries (Aksoy 2005) Amongother conventional crops Korean subsidy policy focuses particularly on rice farming by sup-

18

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

24 Singular Spectrum Analysis

The Singular Spectrum Analysis (SSA) is a method for time series analysis and forecast-ing Since its introduction by Broomhead and King (1986ab) different SSA methodologieshave been developed (eg Golyandina and Zhigljavsky 2013) In this work we use SSA inits basic form (Basic SSA) or repeatedly (Sequential SSA)

Basic SSA is a non-parametric and model-free technique that decomposes a time seriesinto a set of time series such as trend (modulated) periodicities and noise Here we definetrend as any slowly varying time series Thus the main goal of SSA decomposition isobtaining components of the original time series that can be interpreted more easily In thissense Basic SSA can be regarded as a global data-driven frequency decomposition The onlyassumption behind Basic SSA is that the original time series can be represented by a sumof different components (Golyandina and Zhigljavsky 2013) Therefore it can be applied toany time series regardless of its stationarity

We first describe briefly the algorithm of Basic SSA closely following Golyandina andZhigljavsky (2013) and then explain Sequential SSA Basic SSA consists of time series de-composition and reconstruction

Decomposition Consider a real-valued time series XN = (x1 xN) where N is the numberof data points First it is converted into a LtimesK trajectory matrix X

X =

x1 x2 x3 xKx2 x3 x4 xK+1

x3 x4 x5 xK+2

xL xL+1 xL+2 xN

(2)

Its columns consist of lagged vectors of length L of the original time series In other wordsthe trajectory matrix is constructed by moving a window of length L through the time seriesand collecting all K = N minus L+ 1 segments

The second step is the Singular Value Decomposition (SVD) of this trajectory matrix

X = UΛVT (3)

where U and V are the left and right singular vectors respectively and Λ contains d positivesingular values

radicλ1 ge middot middot middot ge

radicλd gt 0 Note that the singular values of X are the square

roots of the eigenvalues of the matrix XXT The collections (radicλi Ui Vi) i = 1 d of

related singular values and singular vectors are called eigentriples

Reconstruction To reconstruct components of the time series we first have to identify whicheigentriples should be grouped together The aim of grouping is to identify the additivecomponents of the time series We partition the set of indices 1 d into m disjointssubsets I1 Im and reconstruct the component time series

XIp =sumiisinIp

radicλiUiV

Ti p = 1 m (4)

6

Thus we obtain the decomposition of the original trajectory matrix

X = XI1 + middot middot middot+ XIm (5)

To recover the additive components of the original time series we have to convert the trajec-tory matrices back to time series by averaging along the secondary diagonals of the matricesXIp

The quality of reconstruction is measured by the ratio of eigenvalues The larger theeigenvalue λi the larger is its ratio λi

sumi λi and the more important is the component for

the reconstruction of the original time series In order for this ratio to be meaningful thetime series should be normalised by subtracting the mean before the SSA (Golyandina andZhigljavsky 2013)

The window length L is a crucial parameter in SSA that strongly influences the decom-position An inappropriate choice of L might lead to separability issues The reconstructedcomponents contain a mixture of different periodicities or periodicities and trend Conse-quently the interpretation of such components is difficult There is no universal rule forchoosing L however some general recommendations exist Usually L le N2 is chosen andmore details can be extracted for larger L If a dominant periodicity T is present (like theyearly cycle) LT should be an integer For small L SSA is equivalent to smoothing witha linear filter of width 2L minus 1 (Golyandina and Zhigljavsky 2013) We chose L = 5 todecompose the short yield time series

The longer price time series showed a complex trend and periodicities For such timeseries the choice of L might become difficult Indeed choosing a large L could mix upperiodicities and trend in the same component On the contrary for a small L periodiccomponents might be inseparable from each other To avoid these separability issues wedecomposed the price time series by Sequential SSA ndash a reiteration of Basic SSA First thetrend is extracted with a small L1 and removed from the original time series Subsequentlythe periodicities are extracted from the residual time series with a larger L2 (Golyandina andZhigljavsky 2013) We chose L1 = 12 and L2 = 48 to extract the trend and the periodicitiesrespectively

Our goal is to compare fluctuations between single crops and crop portfolios It is in-tuitively clear that with respect to revenue stability fluctuations with shorter periods aremore problematic than those with larger periods Therefore we compared the time serieson different time scales For the price data we considered four groups of fluctuations fluc-tuations with periods larger than 24 months (trend) periods of 6ndash24 months (seasonality)3ndash59 months and smaller than 29 months However for the yield data we only distinguishedbetween the trend and the remaining periodicities because the time series were short andconsisted of yearly measurements Different periods for rice and the other crops were chosenas the length of the data was different fluctuations with periods of 23 years and 16 years(trend) for rice and the other crops respectively From now on trend and seasonality willtake on these temporal meanings In the reconstruction step (see above) we grouped theeigentriples according to the dominant periodicity that we calculated from the periodogramof the components A similar approach was used by Mahecha et al (2010) for example tocompare observations with simulated data in biospherendashatmosphere modelling The impor-tance of the fluctuations at a certain time scale is shown by the ratio of the eigenvalues

7

We decomposed the price and the yield of single crops and the price of the crop portfoliosby SSA Because the revenue time series contained only 16 values they were too short foran analysis by SSA All calculations were done in R (R Core Team 2013) using the packageRssa (Korobeynikov 2010 Golyandina and Korobeynikov 2013)

3 Results

31 Farmersrsquo crop selection and empirical crop portfolios

We classified the 218 farmers into three groups based on the number of cultivated cropsGroup 1 included farmers who cultivated one or two crops (n = 44) group 2 those with threeor four crops (n = 100) and group 3 summarised farmers cultivating more than five crops(n = 74) These three groups became the basis of the empirical crop portfolios

The mean age in each group of farmers was 55 54 and 53 for group 1 group 2 and group3 respectively (Table 1) The farming experience increased with the increasing number ofcrops cultivated In group 1 the farm size was smaller compared to the other two groupsThe farm costs (costs of rent labour fertiliser and others) increased with increasing numberof crops which led to lower net income for group 3 with a higher standard deviation Thelevel of education was available as a categorical variable The farmers in group 2 had highereducation compared to the other two groups Note that the total number of farmers in eachgroup was different Among those who had university education 42 of farmers cultivatedmore than five crops

The results of PCA are summarised in Figure 1 and Table 2 The first two principalcomponents (PC) explained approximately 50 of the variance (Supplementary Figure SF6)The first component accounted for 31 of the variance and was positively correlated witheducation and negatively correlated with farming experience The second component ex-plained 189 of the variance and was mainly related to the farm size and the number ofcrops Subsidy was negatively related to PC 2 and had thus an opposite effect comparedto the farm size and the number of crops In other words PC 1 distinguished farmers withmore education and less farming experience from those with less education and more farmingexperience as the main source of variability in the socio-economic background of farmers PC2 contrasted farmers with large farms growing many crops and having less subsidies to thosewith smaller farms and less grown crops having larger subsidies The additional informationregarding the farming management type (eg organic farming partially converted farmingand conventional farming) is supplied in the Supplementary Figure SF2

In total 83 types of crops were cultivated in the watershed of the Soyang Lake in theGangwon Province However 93 of the farmers cultivated one or more crops out of theseven main ones (Table 3) Maize and cabbage shared the same rank However becausemaize is one of the forage crops in South Korea the market conditions differ from othercrops and we excluded it from further analysis Note that in the survey farmers recorded allcrops they planted Therefore the total number of crops and the total number of farmersdiffer

The most critical part of building the empirical crop portfolios was to choose the crops andto decide on their relative contribution In each group of farmers we have selected those whocultivated the smallest number of crops namely one three and five The single crop farmingwas the basis for the comparison Subsequently three- and five-crop portfolios were chosen

8

Tab

le1

Des

crip

tive

stati

stic

sof

farm

ersrsquo

chara

cter

isti

csin

each

gro

up

Gro

up

1a

Gro

up

2b

Gro

up

3c

Tota

l

Conti

nu

ou

sva

riab

les

Aver

age

(sta

nd

ard

dev

iati

on)

Age

(yea

rs)

552

(10

5)54

2(9

8)

539

(82

)54

3(9

4)

Far

min

gex

per

ien

ce(y

ears

)26

6(1

32)

279

(13

2)29

9(1

38)

283

(13

4)F

arm

Siz

e(h

a)2

2(3

3)

31

(32

)3

8(3

9)

32

(35

)T

otal

Cos

tp

erfa

rm(1

00

00

KR

Wd)

121

9(1

691

)3

114

(33

94)

441

5(5

019

)3

165

(39

48)

Rev

enu

ep

erfa

rm(1

000

0K

RW

)3

286

(54

11)

529

0(6

788

)6

363

(54

34)

524

1(6

157

)N

etin

com

ep

erfa

rm(1

00

00K

RW

)2

066

(40

79)

217

6(4

612

)1

947

(37

85)

207

6(4

220

)

Cate

gori

cal

vari

able

sF

requ

ency

(w

ith

inea

chgr

oup

)E

du

cati

onP

rim

ary

school

13(2

95

)26

(26

0)

27(3

65

)66

(30

3)

Sec

on

dary

sch

ool

10(2

27

)38

(38

0)

22(2

97

)70

(32

1)

Hig

hsc

hool

15(3

41

)31

(31

0)

17(2

30

)63

(28

9)

Un

iver

sity

6(1

36

)5

(50

)

8(1

08

)

19(8

7

)

aNumber

ofcrops=

1or2

bNumber

ofcrops=

3or4

cNumber

ofcropsge

5d10000KRW

=853USD

in30th

July

2015

9

minus2 minus1 0 1 2

minus2

0minus

10

00

05

10

PC 1 (31 explained variance)

PC

2 (

189

e

xpla

ined

var

ianc

e)

Education

Age

Farming experience

Farm size (ha)

Number of crops

Subsidy (per ha)

Net income

1minus2 crops3minus4 cropsgt 4 crops

Figure 1 Principal Component Analysis of farmersrsquo characteristics Arrows show original variables Thedirection and the length of the arrows show the correlation between the original variables and the principalcomponents The more an arrow is parallel to the axis the more the original variable is related to thisparticular principal component

Table 2 Loadings from PCA

PC 1 PC 2 PC 3 PC 4 PC 5

Education 0564 0130Age ndash0534 ndash0237 0119 ndash0136 0248Farming experience ndash0569 ndash0218Farm size (ha) 0700 ndash0611Number of crops 0499 ndash0601 0151 0597Subsidy (per ha) 0154 ndash0273 ndash0653 ndash0636 ndash0249Net income 0181 0348 0445 ndash0708 0356

10

Table 3 Number of farmers cultivating the eight main crops in the watershed of the Soyang Lake in theGangwon Province

Rank Crop Number of farmers

1 Pepper 1332 Potato 1163 Beans 904 Ligularia fischeri 645 Rice 596 Radish 527 Cabbage 427 Maize 42

as they were the majorities in each group Then we looked at the most selected crops by eachgroup of farmers Rice was the most frequently cultivated crop by farmers who cultivated asingle crop However as rice is the main staple grain in South Korea rice is highly subsidisedby the government (Korea Rural Economic Institute 2015) which might lead to differentprice conditions compared to the other single crops Therefore we decided not to have riceas a representative crop for the single crop farming but compared all six chosen crops Inthe second group 50 farmers grew three crops most frequently beans pepper and cabbageFinally in the last group among the 25 farmers with five crops potato pepper beanscabbage and Ligularia fischeri dominated However because Ligularia fischeri was relativelynewly introduced to consumers the price data contained large and regularly occurring gaps(Supplementary Table ST1) Therefore SSA could not be carried out for this crop As analternative we have included radish in the five-crop portfolio as the sixth most frequentlychosen crop by farmers who grew five crops We calculated the relative proportions of thesethree or five main crops and composed the empirical crop portfolios as follows

(1) Single crop farming six major crops (100)

(2) Three-crop portfolio beans (350) pepper (325) and cabbage (325)

(3) Five-crop portfolio potato (290) pepper (277) beans (174) cabbage (144)and radish (115)

32 Crop price fluctuations

321 Single crops

Figure 2 shows the variabilities of crop price fluctuations among six main crops in theGangwon Province of South Korea The visual comparison of price data showed that the riceprice was extremely stable compared to any other analysed crops during the study period(Figure 2 and Supplementary Figure SF3 for non-normalised price data) Because rice is themost important cereal crop in South Korea (Korea Rural Economic Institute 2015) severalpolicy instruments such as government buffer stock schemes and direct payments were usedto stabilise the rice price (Park et al 2010) Even though the price for beans was alsorelatively stable a sharp increase was registered in 2004 The price for beans in South Koreais highly dependent on foreign trade and is directly influenced by the global market (OECD

11

Year

Nor

mal

ized

pric

e (K

RW

kg)

minus40

000

2000

6000

1996 1998 2000 2002 2004 2006 2008 2010 2012

ricebeans

potatoradisch

cabbagepepper

Ligularia fischeri

Year

Nor

mal

ized

yie

ld (

ton

ha)

minus15

minus10

minus5

05

1015

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

rice beans potato radisch cabbage pepper

Figure 2 The variability of the normalised crop price (left) and the normalised yield (right) over the analysedperiod The respective mean was subtracted from each time series

2008) Because the US soybean crop yield in 2003 has been the lowest since 1992 theprice in 2004 increased dramatically (USDA 2007) Similarly a large price rise for cabbagewas observed in 2010 although for a different reason (Supplementary Figure SF3 (e) andFigure 2) Due to bad weather in 2010 the supply of cabbage did not meet the demand(Kwon 2012) In comparison to rice and beans the prices for pepper and Ligularia fischerifluctuated strongly

Figure 3 shows the results of the SSA decomposition of the crop prices We consideredfour time scales of fluctuations and evaluated their importance by the ratio of the eigenvalues(cf numbers in parenthesis in Figure 3) These numbers show how much each time scalecontributes to the reconstruction of the original time series We associate the periodicitiesof 24 months and more with a trend and those of 6ndash24 months with seasonal fluctuationsThe third (3ndash59 months) and the fourth (lt 29 months) time scales are however too shortto be interpreted

The prices for rice and beans showed a large contribution of the trend (701 and 546respectively) and a minor one on the smallest time scale (26 and 4 respectively) Thisconfirms the visual impression of stability in Figure 2 Except for rice the crop price datashowed considerable seasonal patterns with the ratio of eigenvalues exceeding 30 Radishand pepper exhibited an especially strong seasonal fluctuation namely 436 and 426respectively Compared to rice and beans cabbage and pepper had a substantial contributionto fluctuations at the smallest time scale (124 and 175 respectively)

322 Crop portfolios

The thee-crop portfolio consisted of beans (35) pepper (325) and cabbage (325)(Figure 4 (a)) The SSA of single crops (Figure 3) showed that the bean price was one ofthe least fluctuating and dominated by the trend whilst pepper and cabbage exhibited alarge seasonal variation The combination of them increased the contribution of the trend(compared to pepper) and decreased the importance of seasonal fluctuations (compared topepper and cabbage) (Figure 4 (a)) However in comparison to the trend-dominated beanprice the fluctuations on all but the largest time scale (trend) increased

The five-crop portfolio included potato (29) pepper (277) beans (174) cabbage(144) and radish (115) (Figure 4 (b)) Compared to the trend-dominated bean price

12

1600

1800

2000

original data gt 24 months (701)(a)

Time

minus50

50

6minus24 months (183)

Time

minus20

20

3minus59 months (89)

Time

minus10

515lt 29 months (26)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

5000

8000

original data gt 24 months (546)(b)

Time

minus20

0020

006minus24 months (303)

Time

minus20

040

0

3minus59 months (111)

Time

minus20

00

200

lt 29 months (4)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

050

015

0025

00

original data gt 24 months (314)(c)

Time

minus40

040

06minus24 months (357)

Time

minus30

030

0 3minus59 months (237)

Time

minus10

020

0lt 29 months (92)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500 original data gt 24 months (238)(d)

Time

minus20

040

06minus24 months (436)

Time

minus20

020

0 3minus59 months (232)

Time

minus10

010

0lt 29 months (95)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500

original data gt 24 months (252)(e)

Time

minus50

050

0

6minus24 months (39)

Time

minus20

020

0 3minus59 months (234)

Time

minus20

020

0

lt 29 months (124)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

6000

1200

0 original data gt 24 months (122)(f)

Time

minus40

0040

006minus24 months (426)

Time

minus20

0020

00 3minus59 months (277)

Time

minus20

0020

00lt 29 months (175)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 3 SSA decomposition of the crop prices (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper Four groups of fluctuation were considered larger than 24 months (trend) 6ndash24 months (sea-sonality) 3ndash59 months smaller than 29 months The number in parenthesis shows the ratio of eigenvaluesThe trend component contains the mean the others show the variability around it

13

1000

3000

5000

original data gt 24 months (239)(a)

Time

minus20

0020

006minus24 months (352)

Time

minus50

050

0 3minus59 months (259)

Timeminus

400

400lt 29 months (15)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

1000

3000

5000

original data gt 24 months (204)(b)

Time

minus20

0020

006minus24 months (408)

Time

minus50

050

0 3minus59 months (236)

Time

minus40

040

0lt 29 months (152)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 4 SSA decomposition of the portfolio prices (a) three-crops portfolio (beans (350) pepper (325)and cabbage (325)) and (b) five-crops portfolio (potato (29) pepper (277) beans (174) cabbage(144) and radish (115))For both portfolio four periods of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it

the contribution of the trend decreased from 546 to 204 Additionally the contributionof the seasonal fluctuation remained comparable to the other crops that have a strong sea-sonal pattern In summary the results of SSA decomposition were similar to the portfoliocomposed of three crops Indeed the summed contributions of the larger time scales (trendand seasonality) as well as those on the smaller time scales differed only slightly

33 Crop yield fluctuations

An in-depth analysis of seasonality was not possible because the time series of yieldconsisted of annual measurements Therefore we only extracted the trend and calculatedthe dominant frequency of the remaining periodicities (Figure 5) The result of SSA showedthat the contribution of the trend varied from 333 to 665 Accordingly the importanceof periodicities ranged from 335 to 667 Their dominant frequency covered 25 years to107 years

In general crop yield had an upwards trend during the analysed period except forradish and cabbage (Figure 5) Four of the six analysed crops namely rice beans potatoand pepper showed increasing trends in the yields In contrast the yield of radish andcabbage had decreased during the 23-year analysed period There were more negative thanpositive extreme values outside the range of the standard deviation of the trend Additionallythe amplitude of negative values was often larger than that of positive values (Figure 5)Interestingly large negative values occurred in different years for different crops In 1980and 1993 for example the rice yield decreased sharply whereas there was a relatively high

14

23

45

6

original data trend (457)(a)

Time

minus2

01

2

25 years (543)

1965 1975 1985 1995 2005

Yie

ld (

ton

ha)

Year

10

12

14

16

18

20

original data trend (333)(b)

Time

minus0

30

00

3

4 years (667)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

1015

2025

3035

40 original data trend (424)(c)

Time

minus10

0527 years (576)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3034

3842 original data trend (349)

(d)

Time

minus6

04

8

46 years (651)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3540

4550

5560 original data trend (344)

(e)

Time

minus10

0523 years (656)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

24

68

1012 original data trend (665)

(f)

Time

minus3

minus1

13

107 years (335)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

Figure 5 SSA decomposition of the crop yield (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper The number in parenthesis shows the ratio of eigenvalues The trend component contains themean the others show the variability around it The yellow area shows plusmn standard deviation around thetrend component Note that the time scale is years and not months as for the price data Fluctuations withperiods of 23 years and 16 years (trend) were chosen for rice and the other crops respectively

15

Year

Rea

l Rev

enue

(M

illio

n K

RW

haminus1

year

minus1)

020

4060

1996 1998 2000 2002 2004 2006 2008 2010

ricebeans

potatoradisch

cabbagepepper

threeminuscrop portfoliofiveminuscrop portfolio

Figure 6 Real revenue for single crops and the empirical crop portfolios

yield in potato in the same year In 1996 the radish yield was very low and the rice yieldmoderately high (See Figure 5 and Supplementary Figure SF4)

The sharp drops of yield often followed damages caused by unusual weather eventsEspecially in 1980 the rice yield reached only 587 of the target yield of South Koreadue to low temperature (Park et al 2010) In 1987 and 2010 radish and cabbage werealso influenced by bad weather (Kwon 2012) Frequent rain and lack of sunlight duringseeding period harmed stabilising seeds (Han and Kim 2010) In addition the yield ofradish and cabbage has declined as the consumption decreases and imports increase (KoreaRural Economic Institute 2015) Actually the import of cabbage has increased since 2003and westernised eating habits of South Koreans has decreased its consumption by 2 peryear since 2002 (Korea Rural Economic Institute 2015)

34 Risk adjusted revenue

The revenue and the Sharpe ratio for each crop portfolio are depicted in Figure 6 andTable 4 The Sharpe ratio is often used to assess the portfolio performance (Blank 1990Roche and McQuinn 2004 Gaydon et al 2012) For example Roche and McQuinn (2004)calculated the Sharpe ratio for the farm land allocation portfolio for grains and Gaydon et al(2012) used it for comparing water management options and their contribution to the farmincome

Figure 6 shows the temporal change of the real revenue of single crops and three-and five-crop portfolios Large differences between the six main crops were observed Rice and beansshowed a stable but the smallest and decreasing revenue compared to the other crops overthe analysed period Pepper showed the highest revenue with the highest standard deviation(Table 4) In the portfolio the mean revenue doubled or tripled and the standard deviationincreased with the number of crops compared to rice and bean single crop farming Althoughthe mean revenue of the crop portfolios was smaller compared to potato and pepper itsstandard deviation decreased The difference between the three- and the five-crop portfoliosin mean and standard deviation was only minor

16

Table 4 Risks adjusted revenue for the analysed period from 1996 to 2011

Crop selection Mean (million KRW) SD Sharpe ratio

Single croprice 1085 173 627

beans 596 175 340potato 3092 770 401radish 1476 298 495

cabbage 2288 435 526pepper 3294 1420 232

three-crop portfolio 2023 532 380five-crop portfolio 2412 560 430

4 Discussion

An advantage of decomposing the time series is that we can not only identify the mostfluctuating crop over time but also quantify different components of fluctuations in eachcrop Fluctuations on larger time scales (trend and seasonality) are easier for farmers toface than short-time variations which are more difficult to address in the planning processIn order to distinguish four time scales of fluctuations in each crop selection we calculatedthe ratio of eigenvalue for each time scale The ratio of eigenvalue stands for the quality ofthe reconstruction of the original time series by a certain component The larger this ratiothe more important the component will be for the reconstruction Among four time scalesthe first and the second scales can be interpreted as trend and seasonality respectively thethird and the fourth scales however were too short to be identified

Farmersrsquo decision on which crop to grow how to allocate the land to grow multiple cropsand when to harvest and sell them plays a crucial role to secure their revenue (Fafchamps1992 Kantanantha et al 2010 Klasen et al 2013) Our result showed that each crop had adifferent fluctuation pattern that highly influenced the farm revenue depending on farmersrsquocrop selection The sum of the first two ratios of eigenvalues for crop price ranged from 548(pepper) to 884 (rice) The larger the contribution of trend and seasonality the less short-time variability is contained in the data Four of the six analysed crops contained notableseasonal patterns The SSA of the three- and the five-crop portfolios also revealed thatimportant seasonal variation still remained in the monthly price data Therefore seasonalityprobably has an important impact on farmersrsquo decisions regarding the times for harvestingor marketing of their crops

The risk adjusted revenue calculated with the Sharpe ratio allows us to compare how muchrevenue standardised per 1 of revenue can be guaranteed for farmers in each crop selectionThe combination of these methods provides more information to support farmersrsquo decision oncrop selection Although the results of SSA and the Sharpe ratio showed that rice and beanfarming were the most stable they provided the lowest revenue The revenue of the three-and the five-crop portfolios was more than two times larger than in rice farming howeverat the same time the standard deviation tripled (Table 4) It indicates that the diversified

17

Time

Pric

e (U

SDto

n)

500

1000

1500

2000

1996 1998 2000 2002 2004 2006 2008 2010 2012

Korean domestic rice price World rice price

200

600

1000 original data gt 24 months (684)

Time

minus10

050

6minus24 months (154)

Time

minus10

00

100

3minus59 months (107)

Time

minus40

040

lt 29 months (54)

1991 1997 2003 2009 2015

Pric

e (U

SD

ton)

Year

Figure 7 Korean domestic rice price converted in USDton and world rice price in USDton (left) SSAdecomposition of the world rice price (right) Four groups of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it The world rice data was Thailand nominal price quote obtained from the World BankGlobal Economic Monitor (GEM) Commodities The exchange rate from Korean Won to USD for each yearwas obtained from the World Bank World Development Indicators

farming could support larger revenue This is in accordance with the study by Bhattacharyya(2008) who showed that a rice dominated farming system in India was changed to high-valuecrops for larger revenue Furthermore an analysis in Argentina showed that diversifiedfarming increased the mean return on capital with a lower coefficient of variation (Pacın andOesterheld 2014) Hence the multiple crop farming may be a means of enhancing revenue(Ali et al 2004 Winters et al 2006 Pacın and Oesterheld 2014 Rahman and Kazal 2015)However the diversification took place slowly due to agricultural subsidies concentrated ona certain crop such as rice in India (Bhattacharyya 2008) This might also be the case inSouth Korea

To examine the artificial stability of the rice price in South Korea we compared thedomestic rice price with the world rice price in USD (Figure 7) As the exchange rate variesbetween years the domestic rice price converted in USD fluctuated more compared to theone in KRW We refer to the SSA result of the rice price in KRW to keep consistency unlessmentioned While the world rice price increased drastically in 2008 as a result of the oilcrisis (Figure 7 right) the Korean domestic price was not affected by it and remained stable(Figure 3 (a)) Overall rice price in the global market fluctuates more than in the SouthKorean domestic market (Baffes and Cosic 2013) Furthermore the Korean domestic priceis more than double or triple the world price ndash the result of a substantial governmentalsupport (Figure 7 left)

South Korea used to have a higher protection for domestic rice farming mainly throughtariff and non-tariff barriers in comparison to other OECD countries (Aksoy 2005) Amongother conventional crops Korean subsidy policy focuses particularly on rice farming by sup-

18

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

Thus we obtain the decomposition of the original trajectory matrix

X = XI1 + middot middot middot+ XIm (5)

To recover the additive components of the original time series we have to convert the trajec-tory matrices back to time series by averaging along the secondary diagonals of the matricesXIp

The quality of reconstruction is measured by the ratio of eigenvalues The larger theeigenvalue λi the larger is its ratio λi

sumi λi and the more important is the component for

the reconstruction of the original time series In order for this ratio to be meaningful thetime series should be normalised by subtracting the mean before the SSA (Golyandina andZhigljavsky 2013)

The window length L is a crucial parameter in SSA that strongly influences the decom-position An inappropriate choice of L might lead to separability issues The reconstructedcomponents contain a mixture of different periodicities or periodicities and trend Conse-quently the interpretation of such components is difficult There is no universal rule forchoosing L however some general recommendations exist Usually L le N2 is chosen andmore details can be extracted for larger L If a dominant periodicity T is present (like theyearly cycle) LT should be an integer For small L SSA is equivalent to smoothing witha linear filter of width 2L minus 1 (Golyandina and Zhigljavsky 2013) We chose L = 5 todecompose the short yield time series

The longer price time series showed a complex trend and periodicities For such timeseries the choice of L might become difficult Indeed choosing a large L could mix upperiodicities and trend in the same component On the contrary for a small L periodiccomponents might be inseparable from each other To avoid these separability issues wedecomposed the price time series by Sequential SSA ndash a reiteration of Basic SSA First thetrend is extracted with a small L1 and removed from the original time series Subsequentlythe periodicities are extracted from the residual time series with a larger L2 (Golyandina andZhigljavsky 2013) We chose L1 = 12 and L2 = 48 to extract the trend and the periodicitiesrespectively

Our goal is to compare fluctuations between single crops and crop portfolios It is in-tuitively clear that with respect to revenue stability fluctuations with shorter periods aremore problematic than those with larger periods Therefore we compared the time serieson different time scales For the price data we considered four groups of fluctuations fluc-tuations with periods larger than 24 months (trend) periods of 6ndash24 months (seasonality)3ndash59 months and smaller than 29 months However for the yield data we only distinguishedbetween the trend and the remaining periodicities because the time series were short andconsisted of yearly measurements Different periods for rice and the other crops were chosenas the length of the data was different fluctuations with periods of 23 years and 16 years(trend) for rice and the other crops respectively From now on trend and seasonality willtake on these temporal meanings In the reconstruction step (see above) we grouped theeigentriples according to the dominant periodicity that we calculated from the periodogramof the components A similar approach was used by Mahecha et al (2010) for example tocompare observations with simulated data in biospherendashatmosphere modelling The impor-tance of the fluctuations at a certain time scale is shown by the ratio of the eigenvalues

7

We decomposed the price and the yield of single crops and the price of the crop portfoliosby SSA Because the revenue time series contained only 16 values they were too short foran analysis by SSA All calculations were done in R (R Core Team 2013) using the packageRssa (Korobeynikov 2010 Golyandina and Korobeynikov 2013)

3 Results

31 Farmersrsquo crop selection and empirical crop portfolios

We classified the 218 farmers into three groups based on the number of cultivated cropsGroup 1 included farmers who cultivated one or two crops (n = 44) group 2 those with threeor four crops (n = 100) and group 3 summarised farmers cultivating more than five crops(n = 74) These three groups became the basis of the empirical crop portfolios

The mean age in each group of farmers was 55 54 and 53 for group 1 group 2 and group3 respectively (Table 1) The farming experience increased with the increasing number ofcrops cultivated In group 1 the farm size was smaller compared to the other two groupsThe farm costs (costs of rent labour fertiliser and others) increased with increasing numberof crops which led to lower net income for group 3 with a higher standard deviation Thelevel of education was available as a categorical variable The farmers in group 2 had highereducation compared to the other two groups Note that the total number of farmers in eachgroup was different Among those who had university education 42 of farmers cultivatedmore than five crops

The results of PCA are summarised in Figure 1 and Table 2 The first two principalcomponents (PC) explained approximately 50 of the variance (Supplementary Figure SF6)The first component accounted for 31 of the variance and was positively correlated witheducation and negatively correlated with farming experience The second component ex-plained 189 of the variance and was mainly related to the farm size and the number ofcrops Subsidy was negatively related to PC 2 and had thus an opposite effect comparedto the farm size and the number of crops In other words PC 1 distinguished farmers withmore education and less farming experience from those with less education and more farmingexperience as the main source of variability in the socio-economic background of farmers PC2 contrasted farmers with large farms growing many crops and having less subsidies to thosewith smaller farms and less grown crops having larger subsidies The additional informationregarding the farming management type (eg organic farming partially converted farmingand conventional farming) is supplied in the Supplementary Figure SF2

In total 83 types of crops were cultivated in the watershed of the Soyang Lake in theGangwon Province However 93 of the farmers cultivated one or more crops out of theseven main ones (Table 3) Maize and cabbage shared the same rank However becausemaize is one of the forage crops in South Korea the market conditions differ from othercrops and we excluded it from further analysis Note that in the survey farmers recorded allcrops they planted Therefore the total number of crops and the total number of farmersdiffer

The most critical part of building the empirical crop portfolios was to choose the crops andto decide on their relative contribution In each group of farmers we have selected those whocultivated the smallest number of crops namely one three and five The single crop farmingwas the basis for the comparison Subsequently three- and five-crop portfolios were chosen

8

Tab

le1

Des

crip

tive

stati

stic

sof

farm

ersrsquo

chara

cter

isti

csin

each

gro

up

Gro

up

1a

Gro

up

2b

Gro

up

3c

Tota

l

Conti

nu

ou

sva

riab

les

Aver

age

(sta

nd

ard

dev

iati

on)

Age

(yea

rs)

552

(10

5)54

2(9

8)

539

(82

)54

3(9

4)

Far

min

gex

per

ien

ce(y

ears

)26

6(1

32)

279

(13

2)29

9(1

38)

283

(13

4)F

arm

Siz

e(h

a)2

2(3

3)

31

(32

)3

8(3

9)

32

(35

)T

otal

Cos

tp

erfa

rm(1

00

00

KR

Wd)

121

9(1

691

)3

114

(33

94)

441

5(5

019

)3

165

(39

48)

Rev

enu

ep

erfa

rm(1

000

0K

RW

)3

286

(54

11)

529

0(6

788

)6

363

(54

34)

524

1(6

157

)N

etin

com

ep

erfa

rm(1

00

00K

RW

)2

066

(40

79)

217

6(4

612

)1

947

(37

85)

207

6(4

220

)

Cate

gori

cal

vari

able

sF

requ

ency

(w

ith

inea

chgr

oup

)E

du

cati

onP

rim

ary

school

13(2

95

)26

(26

0)

27(3

65

)66

(30

3)

Sec

on

dary

sch

ool

10(2

27

)38

(38

0)

22(2

97

)70

(32

1)

Hig

hsc

hool

15(3

41

)31

(31

0)

17(2

30

)63

(28

9)

Un

iver

sity

6(1

36

)5

(50

)

8(1

08

)

19(8

7

)

aNumber

ofcrops=

1or2

bNumber

ofcrops=

3or4

cNumber

ofcropsge

5d10000KRW

=853USD

in30th

July

2015

9

minus2 minus1 0 1 2

minus2

0minus

10

00

05

10

PC 1 (31 explained variance)

PC

2 (

189

e

xpla

ined

var

ianc

e)

Education

Age

Farming experience

Farm size (ha)

Number of crops

Subsidy (per ha)

Net income

1minus2 crops3minus4 cropsgt 4 crops

Figure 1 Principal Component Analysis of farmersrsquo characteristics Arrows show original variables Thedirection and the length of the arrows show the correlation between the original variables and the principalcomponents The more an arrow is parallel to the axis the more the original variable is related to thisparticular principal component

Table 2 Loadings from PCA

PC 1 PC 2 PC 3 PC 4 PC 5

Education 0564 0130Age ndash0534 ndash0237 0119 ndash0136 0248Farming experience ndash0569 ndash0218Farm size (ha) 0700 ndash0611Number of crops 0499 ndash0601 0151 0597Subsidy (per ha) 0154 ndash0273 ndash0653 ndash0636 ndash0249Net income 0181 0348 0445 ndash0708 0356

10

Table 3 Number of farmers cultivating the eight main crops in the watershed of the Soyang Lake in theGangwon Province

Rank Crop Number of farmers

1 Pepper 1332 Potato 1163 Beans 904 Ligularia fischeri 645 Rice 596 Radish 527 Cabbage 427 Maize 42

as they were the majorities in each group Then we looked at the most selected crops by eachgroup of farmers Rice was the most frequently cultivated crop by farmers who cultivated asingle crop However as rice is the main staple grain in South Korea rice is highly subsidisedby the government (Korea Rural Economic Institute 2015) which might lead to differentprice conditions compared to the other single crops Therefore we decided not to have riceas a representative crop for the single crop farming but compared all six chosen crops Inthe second group 50 farmers grew three crops most frequently beans pepper and cabbageFinally in the last group among the 25 farmers with five crops potato pepper beanscabbage and Ligularia fischeri dominated However because Ligularia fischeri was relativelynewly introduced to consumers the price data contained large and regularly occurring gaps(Supplementary Table ST1) Therefore SSA could not be carried out for this crop As analternative we have included radish in the five-crop portfolio as the sixth most frequentlychosen crop by farmers who grew five crops We calculated the relative proportions of thesethree or five main crops and composed the empirical crop portfolios as follows

(1) Single crop farming six major crops (100)

(2) Three-crop portfolio beans (350) pepper (325) and cabbage (325)

(3) Five-crop portfolio potato (290) pepper (277) beans (174) cabbage (144)and radish (115)

32 Crop price fluctuations

321 Single crops

Figure 2 shows the variabilities of crop price fluctuations among six main crops in theGangwon Province of South Korea The visual comparison of price data showed that the riceprice was extremely stable compared to any other analysed crops during the study period(Figure 2 and Supplementary Figure SF3 for non-normalised price data) Because rice is themost important cereal crop in South Korea (Korea Rural Economic Institute 2015) severalpolicy instruments such as government buffer stock schemes and direct payments were usedto stabilise the rice price (Park et al 2010) Even though the price for beans was alsorelatively stable a sharp increase was registered in 2004 The price for beans in South Koreais highly dependent on foreign trade and is directly influenced by the global market (OECD

11

Year

Nor

mal

ized

pric

e (K

RW

kg)

minus40

000

2000

6000

1996 1998 2000 2002 2004 2006 2008 2010 2012

ricebeans

potatoradisch

cabbagepepper

Ligularia fischeri

Year

Nor

mal

ized

yie

ld (

ton

ha)

minus15

minus10

minus5

05

1015

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

rice beans potato radisch cabbage pepper

Figure 2 The variability of the normalised crop price (left) and the normalised yield (right) over the analysedperiod The respective mean was subtracted from each time series

2008) Because the US soybean crop yield in 2003 has been the lowest since 1992 theprice in 2004 increased dramatically (USDA 2007) Similarly a large price rise for cabbagewas observed in 2010 although for a different reason (Supplementary Figure SF3 (e) andFigure 2) Due to bad weather in 2010 the supply of cabbage did not meet the demand(Kwon 2012) In comparison to rice and beans the prices for pepper and Ligularia fischerifluctuated strongly

Figure 3 shows the results of the SSA decomposition of the crop prices We consideredfour time scales of fluctuations and evaluated their importance by the ratio of the eigenvalues(cf numbers in parenthesis in Figure 3) These numbers show how much each time scalecontributes to the reconstruction of the original time series We associate the periodicitiesof 24 months and more with a trend and those of 6ndash24 months with seasonal fluctuationsThe third (3ndash59 months) and the fourth (lt 29 months) time scales are however too shortto be interpreted

The prices for rice and beans showed a large contribution of the trend (701 and 546respectively) and a minor one on the smallest time scale (26 and 4 respectively) Thisconfirms the visual impression of stability in Figure 2 Except for rice the crop price datashowed considerable seasonal patterns with the ratio of eigenvalues exceeding 30 Radishand pepper exhibited an especially strong seasonal fluctuation namely 436 and 426respectively Compared to rice and beans cabbage and pepper had a substantial contributionto fluctuations at the smallest time scale (124 and 175 respectively)

322 Crop portfolios

The thee-crop portfolio consisted of beans (35) pepper (325) and cabbage (325)(Figure 4 (a)) The SSA of single crops (Figure 3) showed that the bean price was one ofthe least fluctuating and dominated by the trend whilst pepper and cabbage exhibited alarge seasonal variation The combination of them increased the contribution of the trend(compared to pepper) and decreased the importance of seasonal fluctuations (compared topepper and cabbage) (Figure 4 (a)) However in comparison to the trend-dominated beanprice the fluctuations on all but the largest time scale (trend) increased

The five-crop portfolio included potato (29) pepper (277) beans (174) cabbage(144) and radish (115) (Figure 4 (b)) Compared to the trend-dominated bean price

12

1600

1800

2000

original data gt 24 months (701)(a)

Time

minus50

50

6minus24 months (183)

Time

minus20

20

3minus59 months (89)

Time

minus10

515lt 29 months (26)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

5000

8000

original data gt 24 months (546)(b)

Time

minus20

0020

006minus24 months (303)

Time

minus20

040

0

3minus59 months (111)

Time

minus20

00

200

lt 29 months (4)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

050

015

0025

00

original data gt 24 months (314)(c)

Time

minus40

040

06minus24 months (357)

Time

minus30

030

0 3minus59 months (237)

Time

minus10

020

0lt 29 months (92)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500 original data gt 24 months (238)(d)

Time

minus20

040

06minus24 months (436)

Time

minus20

020

0 3minus59 months (232)

Time

minus10

010

0lt 29 months (95)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500

original data gt 24 months (252)(e)

Time

minus50

050

0

6minus24 months (39)

Time

minus20

020

0 3minus59 months (234)

Time

minus20

020

0

lt 29 months (124)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

6000

1200

0 original data gt 24 months (122)(f)

Time

minus40

0040

006minus24 months (426)

Time

minus20

0020

00 3minus59 months (277)

Time

minus20

0020

00lt 29 months (175)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 3 SSA decomposition of the crop prices (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper Four groups of fluctuation were considered larger than 24 months (trend) 6ndash24 months (sea-sonality) 3ndash59 months smaller than 29 months The number in parenthesis shows the ratio of eigenvaluesThe trend component contains the mean the others show the variability around it

13

1000

3000

5000

original data gt 24 months (239)(a)

Time

minus20

0020

006minus24 months (352)

Time

minus50

050

0 3minus59 months (259)

Timeminus

400

400lt 29 months (15)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

1000

3000

5000

original data gt 24 months (204)(b)

Time

minus20

0020

006minus24 months (408)

Time

minus50

050

0 3minus59 months (236)

Time

minus40

040

0lt 29 months (152)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 4 SSA decomposition of the portfolio prices (a) three-crops portfolio (beans (350) pepper (325)and cabbage (325)) and (b) five-crops portfolio (potato (29) pepper (277) beans (174) cabbage(144) and radish (115))For both portfolio four periods of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it

the contribution of the trend decreased from 546 to 204 Additionally the contributionof the seasonal fluctuation remained comparable to the other crops that have a strong sea-sonal pattern In summary the results of SSA decomposition were similar to the portfoliocomposed of three crops Indeed the summed contributions of the larger time scales (trendand seasonality) as well as those on the smaller time scales differed only slightly

33 Crop yield fluctuations

An in-depth analysis of seasonality was not possible because the time series of yieldconsisted of annual measurements Therefore we only extracted the trend and calculatedthe dominant frequency of the remaining periodicities (Figure 5) The result of SSA showedthat the contribution of the trend varied from 333 to 665 Accordingly the importanceof periodicities ranged from 335 to 667 Their dominant frequency covered 25 years to107 years

In general crop yield had an upwards trend during the analysed period except forradish and cabbage (Figure 5) Four of the six analysed crops namely rice beans potatoand pepper showed increasing trends in the yields In contrast the yield of radish andcabbage had decreased during the 23-year analysed period There were more negative thanpositive extreme values outside the range of the standard deviation of the trend Additionallythe amplitude of negative values was often larger than that of positive values (Figure 5)Interestingly large negative values occurred in different years for different crops In 1980and 1993 for example the rice yield decreased sharply whereas there was a relatively high

14

23

45

6

original data trend (457)(a)

Time

minus2

01

2

25 years (543)

1965 1975 1985 1995 2005

Yie

ld (

ton

ha)

Year

10

12

14

16

18

20

original data trend (333)(b)

Time

minus0

30

00

3

4 years (667)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

1015

2025

3035

40 original data trend (424)(c)

Time

minus10

0527 years (576)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3034

3842 original data trend (349)

(d)

Time

minus6

04

8

46 years (651)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3540

4550

5560 original data trend (344)

(e)

Time

minus10

0523 years (656)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

24

68

1012 original data trend (665)

(f)

Time

minus3

minus1

13

107 years (335)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

Figure 5 SSA decomposition of the crop yield (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper The number in parenthesis shows the ratio of eigenvalues The trend component contains themean the others show the variability around it The yellow area shows plusmn standard deviation around thetrend component Note that the time scale is years and not months as for the price data Fluctuations withperiods of 23 years and 16 years (trend) were chosen for rice and the other crops respectively

15

Year

Rea

l Rev

enue

(M

illio

n K

RW

haminus1

year

minus1)

020

4060

1996 1998 2000 2002 2004 2006 2008 2010

ricebeans

potatoradisch

cabbagepepper

threeminuscrop portfoliofiveminuscrop portfolio

Figure 6 Real revenue for single crops and the empirical crop portfolios

yield in potato in the same year In 1996 the radish yield was very low and the rice yieldmoderately high (See Figure 5 and Supplementary Figure SF4)

The sharp drops of yield often followed damages caused by unusual weather eventsEspecially in 1980 the rice yield reached only 587 of the target yield of South Koreadue to low temperature (Park et al 2010) In 1987 and 2010 radish and cabbage werealso influenced by bad weather (Kwon 2012) Frequent rain and lack of sunlight duringseeding period harmed stabilising seeds (Han and Kim 2010) In addition the yield ofradish and cabbage has declined as the consumption decreases and imports increase (KoreaRural Economic Institute 2015) Actually the import of cabbage has increased since 2003and westernised eating habits of South Koreans has decreased its consumption by 2 peryear since 2002 (Korea Rural Economic Institute 2015)

34 Risk adjusted revenue

The revenue and the Sharpe ratio for each crop portfolio are depicted in Figure 6 andTable 4 The Sharpe ratio is often used to assess the portfolio performance (Blank 1990Roche and McQuinn 2004 Gaydon et al 2012) For example Roche and McQuinn (2004)calculated the Sharpe ratio for the farm land allocation portfolio for grains and Gaydon et al(2012) used it for comparing water management options and their contribution to the farmincome

Figure 6 shows the temporal change of the real revenue of single crops and three-and five-crop portfolios Large differences between the six main crops were observed Rice and beansshowed a stable but the smallest and decreasing revenue compared to the other crops overthe analysed period Pepper showed the highest revenue with the highest standard deviation(Table 4) In the portfolio the mean revenue doubled or tripled and the standard deviationincreased with the number of crops compared to rice and bean single crop farming Althoughthe mean revenue of the crop portfolios was smaller compared to potato and pepper itsstandard deviation decreased The difference between the three- and the five-crop portfoliosin mean and standard deviation was only minor

16

Table 4 Risks adjusted revenue for the analysed period from 1996 to 2011

Crop selection Mean (million KRW) SD Sharpe ratio

Single croprice 1085 173 627

beans 596 175 340potato 3092 770 401radish 1476 298 495

cabbage 2288 435 526pepper 3294 1420 232

three-crop portfolio 2023 532 380five-crop portfolio 2412 560 430

4 Discussion

An advantage of decomposing the time series is that we can not only identify the mostfluctuating crop over time but also quantify different components of fluctuations in eachcrop Fluctuations on larger time scales (trend and seasonality) are easier for farmers toface than short-time variations which are more difficult to address in the planning processIn order to distinguish four time scales of fluctuations in each crop selection we calculatedthe ratio of eigenvalue for each time scale The ratio of eigenvalue stands for the quality ofthe reconstruction of the original time series by a certain component The larger this ratiothe more important the component will be for the reconstruction Among four time scalesthe first and the second scales can be interpreted as trend and seasonality respectively thethird and the fourth scales however were too short to be identified

Farmersrsquo decision on which crop to grow how to allocate the land to grow multiple cropsand when to harvest and sell them plays a crucial role to secure their revenue (Fafchamps1992 Kantanantha et al 2010 Klasen et al 2013) Our result showed that each crop had adifferent fluctuation pattern that highly influenced the farm revenue depending on farmersrsquocrop selection The sum of the first two ratios of eigenvalues for crop price ranged from 548(pepper) to 884 (rice) The larger the contribution of trend and seasonality the less short-time variability is contained in the data Four of the six analysed crops contained notableseasonal patterns The SSA of the three- and the five-crop portfolios also revealed thatimportant seasonal variation still remained in the monthly price data Therefore seasonalityprobably has an important impact on farmersrsquo decisions regarding the times for harvestingor marketing of their crops

The risk adjusted revenue calculated with the Sharpe ratio allows us to compare how muchrevenue standardised per 1 of revenue can be guaranteed for farmers in each crop selectionThe combination of these methods provides more information to support farmersrsquo decision oncrop selection Although the results of SSA and the Sharpe ratio showed that rice and beanfarming were the most stable they provided the lowest revenue The revenue of the three-and the five-crop portfolios was more than two times larger than in rice farming howeverat the same time the standard deviation tripled (Table 4) It indicates that the diversified

17

Time

Pric

e (U

SDto

n)

500

1000

1500

2000

1996 1998 2000 2002 2004 2006 2008 2010 2012

Korean domestic rice price World rice price

200

600

1000 original data gt 24 months (684)

Time

minus10

050

6minus24 months (154)

Time

minus10

00

100

3minus59 months (107)

Time

minus40

040

lt 29 months (54)

1991 1997 2003 2009 2015

Pric

e (U

SD

ton)

Year

Figure 7 Korean domestic rice price converted in USDton and world rice price in USDton (left) SSAdecomposition of the world rice price (right) Four groups of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it The world rice data was Thailand nominal price quote obtained from the World BankGlobal Economic Monitor (GEM) Commodities The exchange rate from Korean Won to USD for each yearwas obtained from the World Bank World Development Indicators

farming could support larger revenue This is in accordance with the study by Bhattacharyya(2008) who showed that a rice dominated farming system in India was changed to high-valuecrops for larger revenue Furthermore an analysis in Argentina showed that diversifiedfarming increased the mean return on capital with a lower coefficient of variation (Pacın andOesterheld 2014) Hence the multiple crop farming may be a means of enhancing revenue(Ali et al 2004 Winters et al 2006 Pacın and Oesterheld 2014 Rahman and Kazal 2015)However the diversification took place slowly due to agricultural subsidies concentrated ona certain crop such as rice in India (Bhattacharyya 2008) This might also be the case inSouth Korea

To examine the artificial stability of the rice price in South Korea we compared thedomestic rice price with the world rice price in USD (Figure 7) As the exchange rate variesbetween years the domestic rice price converted in USD fluctuated more compared to theone in KRW We refer to the SSA result of the rice price in KRW to keep consistency unlessmentioned While the world rice price increased drastically in 2008 as a result of the oilcrisis (Figure 7 right) the Korean domestic price was not affected by it and remained stable(Figure 3 (a)) Overall rice price in the global market fluctuates more than in the SouthKorean domestic market (Baffes and Cosic 2013) Furthermore the Korean domestic priceis more than double or triple the world price ndash the result of a substantial governmentalsupport (Figure 7 left)

South Korea used to have a higher protection for domestic rice farming mainly throughtariff and non-tariff barriers in comparison to other OECD countries (Aksoy 2005) Amongother conventional crops Korean subsidy policy focuses particularly on rice farming by sup-

18

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

We decomposed the price and the yield of single crops and the price of the crop portfoliosby SSA Because the revenue time series contained only 16 values they were too short foran analysis by SSA All calculations were done in R (R Core Team 2013) using the packageRssa (Korobeynikov 2010 Golyandina and Korobeynikov 2013)

3 Results

31 Farmersrsquo crop selection and empirical crop portfolios

We classified the 218 farmers into three groups based on the number of cultivated cropsGroup 1 included farmers who cultivated one or two crops (n = 44) group 2 those with threeor four crops (n = 100) and group 3 summarised farmers cultivating more than five crops(n = 74) These three groups became the basis of the empirical crop portfolios

The mean age in each group of farmers was 55 54 and 53 for group 1 group 2 and group3 respectively (Table 1) The farming experience increased with the increasing number ofcrops cultivated In group 1 the farm size was smaller compared to the other two groupsThe farm costs (costs of rent labour fertiliser and others) increased with increasing numberof crops which led to lower net income for group 3 with a higher standard deviation Thelevel of education was available as a categorical variable The farmers in group 2 had highereducation compared to the other two groups Note that the total number of farmers in eachgroup was different Among those who had university education 42 of farmers cultivatedmore than five crops

The results of PCA are summarised in Figure 1 and Table 2 The first two principalcomponents (PC) explained approximately 50 of the variance (Supplementary Figure SF6)The first component accounted for 31 of the variance and was positively correlated witheducation and negatively correlated with farming experience The second component ex-plained 189 of the variance and was mainly related to the farm size and the number ofcrops Subsidy was negatively related to PC 2 and had thus an opposite effect comparedto the farm size and the number of crops In other words PC 1 distinguished farmers withmore education and less farming experience from those with less education and more farmingexperience as the main source of variability in the socio-economic background of farmers PC2 contrasted farmers with large farms growing many crops and having less subsidies to thosewith smaller farms and less grown crops having larger subsidies The additional informationregarding the farming management type (eg organic farming partially converted farmingand conventional farming) is supplied in the Supplementary Figure SF2

In total 83 types of crops were cultivated in the watershed of the Soyang Lake in theGangwon Province However 93 of the farmers cultivated one or more crops out of theseven main ones (Table 3) Maize and cabbage shared the same rank However becausemaize is one of the forage crops in South Korea the market conditions differ from othercrops and we excluded it from further analysis Note that in the survey farmers recorded allcrops they planted Therefore the total number of crops and the total number of farmersdiffer

The most critical part of building the empirical crop portfolios was to choose the crops andto decide on their relative contribution In each group of farmers we have selected those whocultivated the smallest number of crops namely one three and five The single crop farmingwas the basis for the comparison Subsequently three- and five-crop portfolios were chosen

8

Tab

le1

Des

crip

tive

stati

stic

sof

farm

ersrsquo

chara

cter

isti

csin

each

gro

up

Gro

up

1a

Gro

up

2b

Gro

up

3c

Tota

l

Conti

nu

ou

sva

riab

les

Aver

age

(sta

nd

ard

dev

iati

on)

Age

(yea

rs)

552

(10

5)54

2(9

8)

539

(82

)54

3(9

4)

Far

min

gex

per

ien

ce(y

ears

)26

6(1

32)

279

(13

2)29

9(1

38)

283

(13

4)F

arm

Siz

e(h

a)2

2(3

3)

31

(32

)3

8(3

9)

32

(35

)T

otal

Cos

tp

erfa

rm(1

00

00

KR

Wd)

121

9(1

691

)3

114

(33

94)

441

5(5

019

)3

165

(39

48)

Rev

enu

ep

erfa

rm(1

000

0K

RW

)3

286

(54

11)

529

0(6

788

)6

363

(54

34)

524

1(6

157

)N

etin

com

ep

erfa

rm(1

00

00K

RW

)2

066

(40

79)

217

6(4

612

)1

947

(37

85)

207

6(4

220

)

Cate

gori

cal

vari

able

sF

requ

ency

(w

ith

inea

chgr

oup

)E

du

cati

onP

rim

ary

school

13(2

95

)26

(26

0)

27(3

65

)66

(30

3)

Sec

on

dary

sch

ool

10(2

27

)38

(38

0)

22(2

97

)70

(32

1)

Hig

hsc

hool

15(3

41

)31

(31

0)

17(2

30

)63

(28

9)

Un

iver

sity

6(1

36

)5

(50

)

8(1

08

)

19(8

7

)

aNumber

ofcrops=

1or2

bNumber

ofcrops=

3or4

cNumber

ofcropsge

5d10000KRW

=853USD

in30th

July

2015

9

minus2 minus1 0 1 2

minus2

0minus

10

00

05

10

PC 1 (31 explained variance)

PC

2 (

189

e

xpla

ined

var

ianc

e)

Education

Age

Farming experience

Farm size (ha)

Number of crops

Subsidy (per ha)

Net income

1minus2 crops3minus4 cropsgt 4 crops

Figure 1 Principal Component Analysis of farmersrsquo characteristics Arrows show original variables Thedirection and the length of the arrows show the correlation between the original variables and the principalcomponents The more an arrow is parallel to the axis the more the original variable is related to thisparticular principal component

Table 2 Loadings from PCA

PC 1 PC 2 PC 3 PC 4 PC 5

Education 0564 0130Age ndash0534 ndash0237 0119 ndash0136 0248Farming experience ndash0569 ndash0218Farm size (ha) 0700 ndash0611Number of crops 0499 ndash0601 0151 0597Subsidy (per ha) 0154 ndash0273 ndash0653 ndash0636 ndash0249Net income 0181 0348 0445 ndash0708 0356

10

Table 3 Number of farmers cultivating the eight main crops in the watershed of the Soyang Lake in theGangwon Province

Rank Crop Number of farmers

1 Pepper 1332 Potato 1163 Beans 904 Ligularia fischeri 645 Rice 596 Radish 527 Cabbage 427 Maize 42

as they were the majorities in each group Then we looked at the most selected crops by eachgroup of farmers Rice was the most frequently cultivated crop by farmers who cultivated asingle crop However as rice is the main staple grain in South Korea rice is highly subsidisedby the government (Korea Rural Economic Institute 2015) which might lead to differentprice conditions compared to the other single crops Therefore we decided not to have riceas a representative crop for the single crop farming but compared all six chosen crops Inthe second group 50 farmers grew three crops most frequently beans pepper and cabbageFinally in the last group among the 25 farmers with five crops potato pepper beanscabbage and Ligularia fischeri dominated However because Ligularia fischeri was relativelynewly introduced to consumers the price data contained large and regularly occurring gaps(Supplementary Table ST1) Therefore SSA could not be carried out for this crop As analternative we have included radish in the five-crop portfolio as the sixth most frequentlychosen crop by farmers who grew five crops We calculated the relative proportions of thesethree or five main crops and composed the empirical crop portfolios as follows

(1) Single crop farming six major crops (100)

(2) Three-crop portfolio beans (350) pepper (325) and cabbage (325)

(3) Five-crop portfolio potato (290) pepper (277) beans (174) cabbage (144)and radish (115)

32 Crop price fluctuations

321 Single crops

Figure 2 shows the variabilities of crop price fluctuations among six main crops in theGangwon Province of South Korea The visual comparison of price data showed that the riceprice was extremely stable compared to any other analysed crops during the study period(Figure 2 and Supplementary Figure SF3 for non-normalised price data) Because rice is themost important cereal crop in South Korea (Korea Rural Economic Institute 2015) severalpolicy instruments such as government buffer stock schemes and direct payments were usedto stabilise the rice price (Park et al 2010) Even though the price for beans was alsorelatively stable a sharp increase was registered in 2004 The price for beans in South Koreais highly dependent on foreign trade and is directly influenced by the global market (OECD

11

Year

Nor

mal

ized

pric

e (K

RW

kg)

minus40

000

2000

6000

1996 1998 2000 2002 2004 2006 2008 2010 2012

ricebeans

potatoradisch

cabbagepepper

Ligularia fischeri

Year

Nor

mal

ized

yie

ld (

ton

ha)

minus15

minus10

minus5

05

1015

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

rice beans potato radisch cabbage pepper

Figure 2 The variability of the normalised crop price (left) and the normalised yield (right) over the analysedperiod The respective mean was subtracted from each time series

2008) Because the US soybean crop yield in 2003 has been the lowest since 1992 theprice in 2004 increased dramatically (USDA 2007) Similarly a large price rise for cabbagewas observed in 2010 although for a different reason (Supplementary Figure SF3 (e) andFigure 2) Due to bad weather in 2010 the supply of cabbage did not meet the demand(Kwon 2012) In comparison to rice and beans the prices for pepper and Ligularia fischerifluctuated strongly

Figure 3 shows the results of the SSA decomposition of the crop prices We consideredfour time scales of fluctuations and evaluated their importance by the ratio of the eigenvalues(cf numbers in parenthesis in Figure 3) These numbers show how much each time scalecontributes to the reconstruction of the original time series We associate the periodicitiesof 24 months and more with a trend and those of 6ndash24 months with seasonal fluctuationsThe third (3ndash59 months) and the fourth (lt 29 months) time scales are however too shortto be interpreted

The prices for rice and beans showed a large contribution of the trend (701 and 546respectively) and a minor one on the smallest time scale (26 and 4 respectively) Thisconfirms the visual impression of stability in Figure 2 Except for rice the crop price datashowed considerable seasonal patterns with the ratio of eigenvalues exceeding 30 Radishand pepper exhibited an especially strong seasonal fluctuation namely 436 and 426respectively Compared to rice and beans cabbage and pepper had a substantial contributionto fluctuations at the smallest time scale (124 and 175 respectively)

322 Crop portfolios

The thee-crop portfolio consisted of beans (35) pepper (325) and cabbage (325)(Figure 4 (a)) The SSA of single crops (Figure 3) showed that the bean price was one ofthe least fluctuating and dominated by the trend whilst pepper and cabbage exhibited alarge seasonal variation The combination of them increased the contribution of the trend(compared to pepper) and decreased the importance of seasonal fluctuations (compared topepper and cabbage) (Figure 4 (a)) However in comparison to the trend-dominated beanprice the fluctuations on all but the largest time scale (trend) increased

The five-crop portfolio included potato (29) pepper (277) beans (174) cabbage(144) and radish (115) (Figure 4 (b)) Compared to the trend-dominated bean price

12

1600

1800

2000

original data gt 24 months (701)(a)

Time

minus50

50

6minus24 months (183)

Time

minus20

20

3minus59 months (89)

Time

minus10

515lt 29 months (26)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

5000

8000

original data gt 24 months (546)(b)

Time

minus20

0020

006minus24 months (303)

Time

minus20

040

0

3minus59 months (111)

Time

minus20

00

200

lt 29 months (4)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

050

015

0025

00

original data gt 24 months (314)(c)

Time

minus40

040

06minus24 months (357)

Time

minus30

030

0 3minus59 months (237)

Time

minus10

020

0lt 29 months (92)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500 original data gt 24 months (238)(d)

Time

minus20

040

06minus24 months (436)

Time

minus20

020

0 3minus59 months (232)

Time

minus10

010

0lt 29 months (95)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500

original data gt 24 months (252)(e)

Time

minus50

050

0

6minus24 months (39)

Time

minus20

020

0 3minus59 months (234)

Time

minus20

020

0

lt 29 months (124)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

6000

1200

0 original data gt 24 months (122)(f)

Time

minus40

0040

006minus24 months (426)

Time

minus20

0020

00 3minus59 months (277)

Time

minus20

0020

00lt 29 months (175)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 3 SSA decomposition of the crop prices (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper Four groups of fluctuation were considered larger than 24 months (trend) 6ndash24 months (sea-sonality) 3ndash59 months smaller than 29 months The number in parenthesis shows the ratio of eigenvaluesThe trend component contains the mean the others show the variability around it

13

1000

3000

5000

original data gt 24 months (239)(a)

Time

minus20

0020

006minus24 months (352)

Time

minus50

050

0 3minus59 months (259)

Timeminus

400

400lt 29 months (15)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

1000

3000

5000

original data gt 24 months (204)(b)

Time

minus20

0020

006minus24 months (408)

Time

minus50

050

0 3minus59 months (236)

Time

minus40

040

0lt 29 months (152)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 4 SSA decomposition of the portfolio prices (a) three-crops portfolio (beans (350) pepper (325)and cabbage (325)) and (b) five-crops portfolio (potato (29) pepper (277) beans (174) cabbage(144) and radish (115))For both portfolio four periods of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it

the contribution of the trend decreased from 546 to 204 Additionally the contributionof the seasonal fluctuation remained comparable to the other crops that have a strong sea-sonal pattern In summary the results of SSA decomposition were similar to the portfoliocomposed of three crops Indeed the summed contributions of the larger time scales (trendand seasonality) as well as those on the smaller time scales differed only slightly

33 Crop yield fluctuations

An in-depth analysis of seasonality was not possible because the time series of yieldconsisted of annual measurements Therefore we only extracted the trend and calculatedthe dominant frequency of the remaining periodicities (Figure 5) The result of SSA showedthat the contribution of the trend varied from 333 to 665 Accordingly the importanceof periodicities ranged from 335 to 667 Their dominant frequency covered 25 years to107 years

In general crop yield had an upwards trend during the analysed period except forradish and cabbage (Figure 5) Four of the six analysed crops namely rice beans potatoand pepper showed increasing trends in the yields In contrast the yield of radish andcabbage had decreased during the 23-year analysed period There were more negative thanpositive extreme values outside the range of the standard deviation of the trend Additionallythe amplitude of negative values was often larger than that of positive values (Figure 5)Interestingly large negative values occurred in different years for different crops In 1980and 1993 for example the rice yield decreased sharply whereas there was a relatively high

14

23

45

6

original data trend (457)(a)

Time

minus2

01

2

25 years (543)

1965 1975 1985 1995 2005

Yie

ld (

ton

ha)

Year

10

12

14

16

18

20

original data trend (333)(b)

Time

minus0

30

00

3

4 years (667)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

1015

2025

3035

40 original data trend (424)(c)

Time

minus10

0527 years (576)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3034

3842 original data trend (349)

(d)

Time

minus6

04

8

46 years (651)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3540

4550

5560 original data trend (344)

(e)

Time

minus10

0523 years (656)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

24

68

1012 original data trend (665)

(f)

Time

minus3

minus1

13

107 years (335)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

Figure 5 SSA decomposition of the crop yield (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper The number in parenthesis shows the ratio of eigenvalues The trend component contains themean the others show the variability around it The yellow area shows plusmn standard deviation around thetrend component Note that the time scale is years and not months as for the price data Fluctuations withperiods of 23 years and 16 years (trend) were chosen for rice and the other crops respectively

15

Year

Rea

l Rev

enue

(M

illio

n K

RW

haminus1

year

minus1)

020

4060

1996 1998 2000 2002 2004 2006 2008 2010

ricebeans

potatoradisch

cabbagepepper

threeminuscrop portfoliofiveminuscrop portfolio

Figure 6 Real revenue for single crops and the empirical crop portfolios

yield in potato in the same year In 1996 the radish yield was very low and the rice yieldmoderately high (See Figure 5 and Supplementary Figure SF4)

The sharp drops of yield often followed damages caused by unusual weather eventsEspecially in 1980 the rice yield reached only 587 of the target yield of South Koreadue to low temperature (Park et al 2010) In 1987 and 2010 radish and cabbage werealso influenced by bad weather (Kwon 2012) Frequent rain and lack of sunlight duringseeding period harmed stabilising seeds (Han and Kim 2010) In addition the yield ofradish and cabbage has declined as the consumption decreases and imports increase (KoreaRural Economic Institute 2015) Actually the import of cabbage has increased since 2003and westernised eating habits of South Koreans has decreased its consumption by 2 peryear since 2002 (Korea Rural Economic Institute 2015)

34 Risk adjusted revenue

The revenue and the Sharpe ratio for each crop portfolio are depicted in Figure 6 andTable 4 The Sharpe ratio is often used to assess the portfolio performance (Blank 1990Roche and McQuinn 2004 Gaydon et al 2012) For example Roche and McQuinn (2004)calculated the Sharpe ratio for the farm land allocation portfolio for grains and Gaydon et al(2012) used it for comparing water management options and their contribution to the farmincome

Figure 6 shows the temporal change of the real revenue of single crops and three-and five-crop portfolios Large differences between the six main crops were observed Rice and beansshowed a stable but the smallest and decreasing revenue compared to the other crops overthe analysed period Pepper showed the highest revenue with the highest standard deviation(Table 4) In the portfolio the mean revenue doubled or tripled and the standard deviationincreased with the number of crops compared to rice and bean single crop farming Althoughthe mean revenue of the crop portfolios was smaller compared to potato and pepper itsstandard deviation decreased The difference between the three- and the five-crop portfoliosin mean and standard deviation was only minor

16

Table 4 Risks adjusted revenue for the analysed period from 1996 to 2011

Crop selection Mean (million KRW) SD Sharpe ratio

Single croprice 1085 173 627

beans 596 175 340potato 3092 770 401radish 1476 298 495

cabbage 2288 435 526pepper 3294 1420 232

three-crop portfolio 2023 532 380five-crop portfolio 2412 560 430

4 Discussion

An advantage of decomposing the time series is that we can not only identify the mostfluctuating crop over time but also quantify different components of fluctuations in eachcrop Fluctuations on larger time scales (trend and seasonality) are easier for farmers toface than short-time variations which are more difficult to address in the planning processIn order to distinguish four time scales of fluctuations in each crop selection we calculatedthe ratio of eigenvalue for each time scale The ratio of eigenvalue stands for the quality ofthe reconstruction of the original time series by a certain component The larger this ratiothe more important the component will be for the reconstruction Among four time scalesthe first and the second scales can be interpreted as trend and seasonality respectively thethird and the fourth scales however were too short to be identified

Farmersrsquo decision on which crop to grow how to allocate the land to grow multiple cropsand when to harvest and sell them plays a crucial role to secure their revenue (Fafchamps1992 Kantanantha et al 2010 Klasen et al 2013) Our result showed that each crop had adifferent fluctuation pattern that highly influenced the farm revenue depending on farmersrsquocrop selection The sum of the first two ratios of eigenvalues for crop price ranged from 548(pepper) to 884 (rice) The larger the contribution of trend and seasonality the less short-time variability is contained in the data Four of the six analysed crops contained notableseasonal patterns The SSA of the three- and the five-crop portfolios also revealed thatimportant seasonal variation still remained in the monthly price data Therefore seasonalityprobably has an important impact on farmersrsquo decisions regarding the times for harvestingor marketing of their crops

The risk adjusted revenue calculated with the Sharpe ratio allows us to compare how muchrevenue standardised per 1 of revenue can be guaranteed for farmers in each crop selectionThe combination of these methods provides more information to support farmersrsquo decision oncrop selection Although the results of SSA and the Sharpe ratio showed that rice and beanfarming were the most stable they provided the lowest revenue The revenue of the three-and the five-crop portfolios was more than two times larger than in rice farming howeverat the same time the standard deviation tripled (Table 4) It indicates that the diversified

17

Time

Pric

e (U

SDto

n)

500

1000

1500

2000

1996 1998 2000 2002 2004 2006 2008 2010 2012

Korean domestic rice price World rice price

200

600

1000 original data gt 24 months (684)

Time

minus10

050

6minus24 months (154)

Time

minus10

00

100

3minus59 months (107)

Time

minus40

040

lt 29 months (54)

1991 1997 2003 2009 2015

Pric

e (U

SD

ton)

Year

Figure 7 Korean domestic rice price converted in USDton and world rice price in USDton (left) SSAdecomposition of the world rice price (right) Four groups of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it The world rice data was Thailand nominal price quote obtained from the World BankGlobal Economic Monitor (GEM) Commodities The exchange rate from Korean Won to USD for each yearwas obtained from the World Bank World Development Indicators

farming could support larger revenue This is in accordance with the study by Bhattacharyya(2008) who showed that a rice dominated farming system in India was changed to high-valuecrops for larger revenue Furthermore an analysis in Argentina showed that diversifiedfarming increased the mean return on capital with a lower coefficient of variation (Pacın andOesterheld 2014) Hence the multiple crop farming may be a means of enhancing revenue(Ali et al 2004 Winters et al 2006 Pacın and Oesterheld 2014 Rahman and Kazal 2015)However the diversification took place slowly due to agricultural subsidies concentrated ona certain crop such as rice in India (Bhattacharyya 2008) This might also be the case inSouth Korea

To examine the artificial stability of the rice price in South Korea we compared thedomestic rice price with the world rice price in USD (Figure 7) As the exchange rate variesbetween years the domestic rice price converted in USD fluctuated more compared to theone in KRW We refer to the SSA result of the rice price in KRW to keep consistency unlessmentioned While the world rice price increased drastically in 2008 as a result of the oilcrisis (Figure 7 right) the Korean domestic price was not affected by it and remained stable(Figure 3 (a)) Overall rice price in the global market fluctuates more than in the SouthKorean domestic market (Baffes and Cosic 2013) Furthermore the Korean domestic priceis more than double or triple the world price ndash the result of a substantial governmentalsupport (Figure 7 left)

South Korea used to have a higher protection for domestic rice farming mainly throughtariff and non-tariff barriers in comparison to other OECD countries (Aksoy 2005) Amongother conventional crops Korean subsidy policy focuses particularly on rice farming by sup-

18

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

Tab

le1

Des

crip

tive

stati

stic

sof

farm

ersrsquo

chara

cter

isti

csin

each

gro

up

Gro

up

1a

Gro

up

2b

Gro

up

3c

Tota

l

Conti

nu

ou

sva

riab

les

Aver

age

(sta

nd

ard

dev

iati

on)

Age

(yea

rs)

552

(10

5)54

2(9

8)

539

(82

)54

3(9

4)

Far

min

gex

per

ien

ce(y

ears

)26

6(1

32)

279

(13

2)29

9(1

38)

283

(13

4)F

arm

Siz

e(h

a)2

2(3

3)

31

(32

)3

8(3

9)

32

(35

)T

otal

Cos

tp

erfa

rm(1

00

00

KR

Wd)

121

9(1

691

)3

114

(33

94)

441

5(5

019

)3

165

(39

48)

Rev

enu

ep

erfa

rm(1

000

0K

RW

)3

286

(54

11)

529

0(6

788

)6

363

(54

34)

524

1(6

157

)N

etin

com

ep

erfa

rm(1

00

00K

RW

)2

066

(40

79)

217

6(4

612

)1

947

(37

85)

207

6(4

220

)

Cate

gori

cal

vari

able

sF

requ

ency

(w

ith

inea

chgr

oup

)E

du

cati

onP

rim

ary

school

13(2

95

)26

(26

0)

27(3

65

)66

(30

3)

Sec

on

dary

sch

ool

10(2

27

)38

(38

0)

22(2

97

)70

(32

1)

Hig

hsc

hool

15(3

41

)31

(31

0)

17(2

30

)63

(28

9)

Un

iver

sity

6(1

36

)5

(50

)

8(1

08

)

19(8

7

)

aNumber

ofcrops=

1or2

bNumber

ofcrops=

3or4

cNumber

ofcropsge

5d10000KRW

=853USD

in30th

July

2015

9

minus2 minus1 0 1 2

minus2

0minus

10

00

05

10

PC 1 (31 explained variance)

PC

2 (

189

e

xpla

ined

var

ianc

e)

Education

Age

Farming experience

Farm size (ha)

Number of crops

Subsidy (per ha)

Net income

1minus2 crops3minus4 cropsgt 4 crops

Figure 1 Principal Component Analysis of farmersrsquo characteristics Arrows show original variables Thedirection and the length of the arrows show the correlation between the original variables and the principalcomponents The more an arrow is parallel to the axis the more the original variable is related to thisparticular principal component

Table 2 Loadings from PCA

PC 1 PC 2 PC 3 PC 4 PC 5

Education 0564 0130Age ndash0534 ndash0237 0119 ndash0136 0248Farming experience ndash0569 ndash0218Farm size (ha) 0700 ndash0611Number of crops 0499 ndash0601 0151 0597Subsidy (per ha) 0154 ndash0273 ndash0653 ndash0636 ndash0249Net income 0181 0348 0445 ndash0708 0356

10

Table 3 Number of farmers cultivating the eight main crops in the watershed of the Soyang Lake in theGangwon Province

Rank Crop Number of farmers

1 Pepper 1332 Potato 1163 Beans 904 Ligularia fischeri 645 Rice 596 Radish 527 Cabbage 427 Maize 42

as they were the majorities in each group Then we looked at the most selected crops by eachgroup of farmers Rice was the most frequently cultivated crop by farmers who cultivated asingle crop However as rice is the main staple grain in South Korea rice is highly subsidisedby the government (Korea Rural Economic Institute 2015) which might lead to differentprice conditions compared to the other single crops Therefore we decided not to have riceas a representative crop for the single crop farming but compared all six chosen crops Inthe second group 50 farmers grew three crops most frequently beans pepper and cabbageFinally in the last group among the 25 farmers with five crops potato pepper beanscabbage and Ligularia fischeri dominated However because Ligularia fischeri was relativelynewly introduced to consumers the price data contained large and regularly occurring gaps(Supplementary Table ST1) Therefore SSA could not be carried out for this crop As analternative we have included radish in the five-crop portfolio as the sixth most frequentlychosen crop by farmers who grew five crops We calculated the relative proportions of thesethree or five main crops and composed the empirical crop portfolios as follows

(1) Single crop farming six major crops (100)

(2) Three-crop portfolio beans (350) pepper (325) and cabbage (325)

(3) Five-crop portfolio potato (290) pepper (277) beans (174) cabbage (144)and radish (115)

32 Crop price fluctuations

321 Single crops

Figure 2 shows the variabilities of crop price fluctuations among six main crops in theGangwon Province of South Korea The visual comparison of price data showed that the riceprice was extremely stable compared to any other analysed crops during the study period(Figure 2 and Supplementary Figure SF3 for non-normalised price data) Because rice is themost important cereal crop in South Korea (Korea Rural Economic Institute 2015) severalpolicy instruments such as government buffer stock schemes and direct payments were usedto stabilise the rice price (Park et al 2010) Even though the price for beans was alsorelatively stable a sharp increase was registered in 2004 The price for beans in South Koreais highly dependent on foreign trade and is directly influenced by the global market (OECD

11

Year

Nor

mal

ized

pric

e (K

RW

kg)

minus40

000

2000

6000

1996 1998 2000 2002 2004 2006 2008 2010 2012

ricebeans

potatoradisch

cabbagepepper

Ligularia fischeri

Year

Nor

mal

ized

yie

ld (

ton

ha)

minus15

minus10

minus5

05

1015

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

rice beans potato radisch cabbage pepper

Figure 2 The variability of the normalised crop price (left) and the normalised yield (right) over the analysedperiod The respective mean was subtracted from each time series

2008) Because the US soybean crop yield in 2003 has been the lowest since 1992 theprice in 2004 increased dramatically (USDA 2007) Similarly a large price rise for cabbagewas observed in 2010 although for a different reason (Supplementary Figure SF3 (e) andFigure 2) Due to bad weather in 2010 the supply of cabbage did not meet the demand(Kwon 2012) In comparison to rice and beans the prices for pepper and Ligularia fischerifluctuated strongly

Figure 3 shows the results of the SSA decomposition of the crop prices We consideredfour time scales of fluctuations and evaluated their importance by the ratio of the eigenvalues(cf numbers in parenthesis in Figure 3) These numbers show how much each time scalecontributes to the reconstruction of the original time series We associate the periodicitiesof 24 months and more with a trend and those of 6ndash24 months with seasonal fluctuationsThe third (3ndash59 months) and the fourth (lt 29 months) time scales are however too shortto be interpreted

The prices for rice and beans showed a large contribution of the trend (701 and 546respectively) and a minor one on the smallest time scale (26 and 4 respectively) Thisconfirms the visual impression of stability in Figure 2 Except for rice the crop price datashowed considerable seasonal patterns with the ratio of eigenvalues exceeding 30 Radishand pepper exhibited an especially strong seasonal fluctuation namely 436 and 426respectively Compared to rice and beans cabbage and pepper had a substantial contributionto fluctuations at the smallest time scale (124 and 175 respectively)

322 Crop portfolios

The thee-crop portfolio consisted of beans (35) pepper (325) and cabbage (325)(Figure 4 (a)) The SSA of single crops (Figure 3) showed that the bean price was one ofthe least fluctuating and dominated by the trend whilst pepper and cabbage exhibited alarge seasonal variation The combination of them increased the contribution of the trend(compared to pepper) and decreased the importance of seasonal fluctuations (compared topepper and cabbage) (Figure 4 (a)) However in comparison to the trend-dominated beanprice the fluctuations on all but the largest time scale (trend) increased

The five-crop portfolio included potato (29) pepper (277) beans (174) cabbage(144) and radish (115) (Figure 4 (b)) Compared to the trend-dominated bean price

12

1600

1800

2000

original data gt 24 months (701)(a)

Time

minus50

50

6minus24 months (183)

Time

minus20

20

3minus59 months (89)

Time

minus10

515lt 29 months (26)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

5000

8000

original data gt 24 months (546)(b)

Time

minus20

0020

006minus24 months (303)

Time

minus20

040

0

3minus59 months (111)

Time

minus20

00

200

lt 29 months (4)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

050

015

0025

00

original data gt 24 months (314)(c)

Time

minus40

040

06minus24 months (357)

Time

minus30

030

0 3minus59 months (237)

Time

minus10

020

0lt 29 months (92)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500 original data gt 24 months (238)(d)

Time

minus20

040

06minus24 months (436)

Time

minus20

020

0 3minus59 months (232)

Time

minus10

010

0lt 29 months (95)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500

original data gt 24 months (252)(e)

Time

minus50

050

0

6minus24 months (39)

Time

minus20

020

0 3minus59 months (234)

Time

minus20

020

0

lt 29 months (124)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

6000

1200

0 original data gt 24 months (122)(f)

Time

minus40

0040

006minus24 months (426)

Time

minus20

0020

00 3minus59 months (277)

Time

minus20

0020

00lt 29 months (175)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 3 SSA decomposition of the crop prices (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper Four groups of fluctuation were considered larger than 24 months (trend) 6ndash24 months (sea-sonality) 3ndash59 months smaller than 29 months The number in parenthesis shows the ratio of eigenvaluesThe trend component contains the mean the others show the variability around it

13

1000

3000

5000

original data gt 24 months (239)(a)

Time

minus20

0020

006minus24 months (352)

Time

minus50

050

0 3minus59 months (259)

Timeminus

400

400lt 29 months (15)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

1000

3000

5000

original data gt 24 months (204)(b)

Time

minus20

0020

006minus24 months (408)

Time

minus50

050

0 3minus59 months (236)

Time

minus40

040

0lt 29 months (152)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 4 SSA decomposition of the portfolio prices (a) three-crops portfolio (beans (350) pepper (325)and cabbage (325)) and (b) five-crops portfolio (potato (29) pepper (277) beans (174) cabbage(144) and radish (115))For both portfolio four periods of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it

the contribution of the trend decreased from 546 to 204 Additionally the contributionof the seasonal fluctuation remained comparable to the other crops that have a strong sea-sonal pattern In summary the results of SSA decomposition were similar to the portfoliocomposed of three crops Indeed the summed contributions of the larger time scales (trendand seasonality) as well as those on the smaller time scales differed only slightly

33 Crop yield fluctuations

An in-depth analysis of seasonality was not possible because the time series of yieldconsisted of annual measurements Therefore we only extracted the trend and calculatedthe dominant frequency of the remaining periodicities (Figure 5) The result of SSA showedthat the contribution of the trend varied from 333 to 665 Accordingly the importanceof periodicities ranged from 335 to 667 Their dominant frequency covered 25 years to107 years

In general crop yield had an upwards trend during the analysed period except forradish and cabbage (Figure 5) Four of the six analysed crops namely rice beans potatoand pepper showed increasing trends in the yields In contrast the yield of radish andcabbage had decreased during the 23-year analysed period There were more negative thanpositive extreme values outside the range of the standard deviation of the trend Additionallythe amplitude of negative values was often larger than that of positive values (Figure 5)Interestingly large negative values occurred in different years for different crops In 1980and 1993 for example the rice yield decreased sharply whereas there was a relatively high

14

23

45

6

original data trend (457)(a)

Time

minus2

01

2

25 years (543)

1965 1975 1985 1995 2005

Yie

ld (

ton

ha)

Year

10

12

14

16

18

20

original data trend (333)(b)

Time

minus0

30

00

3

4 years (667)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

1015

2025

3035

40 original data trend (424)(c)

Time

minus10

0527 years (576)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3034

3842 original data trend (349)

(d)

Time

minus6

04

8

46 years (651)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3540

4550

5560 original data trend (344)

(e)

Time

minus10

0523 years (656)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

24

68

1012 original data trend (665)

(f)

Time

minus3

minus1

13

107 years (335)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

Figure 5 SSA decomposition of the crop yield (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper The number in parenthesis shows the ratio of eigenvalues The trend component contains themean the others show the variability around it The yellow area shows plusmn standard deviation around thetrend component Note that the time scale is years and not months as for the price data Fluctuations withperiods of 23 years and 16 years (trend) were chosen for rice and the other crops respectively

15

Year

Rea

l Rev

enue

(M

illio

n K

RW

haminus1

year

minus1)

020

4060

1996 1998 2000 2002 2004 2006 2008 2010

ricebeans

potatoradisch

cabbagepepper

threeminuscrop portfoliofiveminuscrop portfolio

Figure 6 Real revenue for single crops and the empirical crop portfolios

yield in potato in the same year In 1996 the radish yield was very low and the rice yieldmoderately high (See Figure 5 and Supplementary Figure SF4)

The sharp drops of yield often followed damages caused by unusual weather eventsEspecially in 1980 the rice yield reached only 587 of the target yield of South Koreadue to low temperature (Park et al 2010) In 1987 and 2010 radish and cabbage werealso influenced by bad weather (Kwon 2012) Frequent rain and lack of sunlight duringseeding period harmed stabilising seeds (Han and Kim 2010) In addition the yield ofradish and cabbage has declined as the consumption decreases and imports increase (KoreaRural Economic Institute 2015) Actually the import of cabbage has increased since 2003and westernised eating habits of South Koreans has decreased its consumption by 2 peryear since 2002 (Korea Rural Economic Institute 2015)

34 Risk adjusted revenue

The revenue and the Sharpe ratio for each crop portfolio are depicted in Figure 6 andTable 4 The Sharpe ratio is often used to assess the portfolio performance (Blank 1990Roche and McQuinn 2004 Gaydon et al 2012) For example Roche and McQuinn (2004)calculated the Sharpe ratio for the farm land allocation portfolio for grains and Gaydon et al(2012) used it for comparing water management options and their contribution to the farmincome

Figure 6 shows the temporal change of the real revenue of single crops and three-and five-crop portfolios Large differences between the six main crops were observed Rice and beansshowed a stable but the smallest and decreasing revenue compared to the other crops overthe analysed period Pepper showed the highest revenue with the highest standard deviation(Table 4) In the portfolio the mean revenue doubled or tripled and the standard deviationincreased with the number of crops compared to rice and bean single crop farming Althoughthe mean revenue of the crop portfolios was smaller compared to potato and pepper itsstandard deviation decreased The difference between the three- and the five-crop portfoliosin mean and standard deviation was only minor

16

Table 4 Risks adjusted revenue for the analysed period from 1996 to 2011

Crop selection Mean (million KRW) SD Sharpe ratio

Single croprice 1085 173 627

beans 596 175 340potato 3092 770 401radish 1476 298 495

cabbage 2288 435 526pepper 3294 1420 232

three-crop portfolio 2023 532 380five-crop portfolio 2412 560 430

4 Discussion

An advantage of decomposing the time series is that we can not only identify the mostfluctuating crop over time but also quantify different components of fluctuations in eachcrop Fluctuations on larger time scales (trend and seasonality) are easier for farmers toface than short-time variations which are more difficult to address in the planning processIn order to distinguish four time scales of fluctuations in each crop selection we calculatedthe ratio of eigenvalue for each time scale The ratio of eigenvalue stands for the quality ofthe reconstruction of the original time series by a certain component The larger this ratiothe more important the component will be for the reconstruction Among four time scalesthe first and the second scales can be interpreted as trend and seasonality respectively thethird and the fourth scales however were too short to be identified

Farmersrsquo decision on which crop to grow how to allocate the land to grow multiple cropsand when to harvest and sell them plays a crucial role to secure their revenue (Fafchamps1992 Kantanantha et al 2010 Klasen et al 2013) Our result showed that each crop had adifferent fluctuation pattern that highly influenced the farm revenue depending on farmersrsquocrop selection The sum of the first two ratios of eigenvalues for crop price ranged from 548(pepper) to 884 (rice) The larger the contribution of trend and seasonality the less short-time variability is contained in the data Four of the six analysed crops contained notableseasonal patterns The SSA of the three- and the five-crop portfolios also revealed thatimportant seasonal variation still remained in the monthly price data Therefore seasonalityprobably has an important impact on farmersrsquo decisions regarding the times for harvestingor marketing of their crops

The risk adjusted revenue calculated with the Sharpe ratio allows us to compare how muchrevenue standardised per 1 of revenue can be guaranteed for farmers in each crop selectionThe combination of these methods provides more information to support farmersrsquo decision oncrop selection Although the results of SSA and the Sharpe ratio showed that rice and beanfarming were the most stable they provided the lowest revenue The revenue of the three-and the five-crop portfolios was more than two times larger than in rice farming howeverat the same time the standard deviation tripled (Table 4) It indicates that the diversified

17

Time

Pric

e (U

SDto

n)

500

1000

1500

2000

1996 1998 2000 2002 2004 2006 2008 2010 2012

Korean domestic rice price World rice price

200

600

1000 original data gt 24 months (684)

Time

minus10

050

6minus24 months (154)

Time

minus10

00

100

3minus59 months (107)

Time

minus40

040

lt 29 months (54)

1991 1997 2003 2009 2015

Pric

e (U

SD

ton)

Year

Figure 7 Korean domestic rice price converted in USDton and world rice price in USDton (left) SSAdecomposition of the world rice price (right) Four groups of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it The world rice data was Thailand nominal price quote obtained from the World BankGlobal Economic Monitor (GEM) Commodities The exchange rate from Korean Won to USD for each yearwas obtained from the World Bank World Development Indicators

farming could support larger revenue This is in accordance with the study by Bhattacharyya(2008) who showed that a rice dominated farming system in India was changed to high-valuecrops for larger revenue Furthermore an analysis in Argentina showed that diversifiedfarming increased the mean return on capital with a lower coefficient of variation (Pacın andOesterheld 2014) Hence the multiple crop farming may be a means of enhancing revenue(Ali et al 2004 Winters et al 2006 Pacın and Oesterheld 2014 Rahman and Kazal 2015)However the diversification took place slowly due to agricultural subsidies concentrated ona certain crop such as rice in India (Bhattacharyya 2008) This might also be the case inSouth Korea

To examine the artificial stability of the rice price in South Korea we compared thedomestic rice price with the world rice price in USD (Figure 7) As the exchange rate variesbetween years the domestic rice price converted in USD fluctuated more compared to theone in KRW We refer to the SSA result of the rice price in KRW to keep consistency unlessmentioned While the world rice price increased drastically in 2008 as a result of the oilcrisis (Figure 7 right) the Korean domestic price was not affected by it and remained stable(Figure 3 (a)) Overall rice price in the global market fluctuates more than in the SouthKorean domestic market (Baffes and Cosic 2013) Furthermore the Korean domestic priceis more than double or triple the world price ndash the result of a substantial governmentalsupport (Figure 7 left)

South Korea used to have a higher protection for domestic rice farming mainly throughtariff and non-tariff barriers in comparison to other OECD countries (Aksoy 2005) Amongother conventional crops Korean subsidy policy focuses particularly on rice farming by sup-

18

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

minus2 minus1 0 1 2

minus2

0minus

10

00

05

10

PC 1 (31 explained variance)

PC

2 (

189

e

xpla

ined

var

ianc

e)

Education

Age

Farming experience

Farm size (ha)

Number of crops

Subsidy (per ha)

Net income

1minus2 crops3minus4 cropsgt 4 crops

Figure 1 Principal Component Analysis of farmersrsquo characteristics Arrows show original variables Thedirection and the length of the arrows show the correlation between the original variables and the principalcomponents The more an arrow is parallel to the axis the more the original variable is related to thisparticular principal component

Table 2 Loadings from PCA

PC 1 PC 2 PC 3 PC 4 PC 5

Education 0564 0130Age ndash0534 ndash0237 0119 ndash0136 0248Farming experience ndash0569 ndash0218Farm size (ha) 0700 ndash0611Number of crops 0499 ndash0601 0151 0597Subsidy (per ha) 0154 ndash0273 ndash0653 ndash0636 ndash0249Net income 0181 0348 0445 ndash0708 0356

10

Table 3 Number of farmers cultivating the eight main crops in the watershed of the Soyang Lake in theGangwon Province

Rank Crop Number of farmers

1 Pepper 1332 Potato 1163 Beans 904 Ligularia fischeri 645 Rice 596 Radish 527 Cabbage 427 Maize 42

as they were the majorities in each group Then we looked at the most selected crops by eachgroup of farmers Rice was the most frequently cultivated crop by farmers who cultivated asingle crop However as rice is the main staple grain in South Korea rice is highly subsidisedby the government (Korea Rural Economic Institute 2015) which might lead to differentprice conditions compared to the other single crops Therefore we decided not to have riceas a representative crop for the single crop farming but compared all six chosen crops Inthe second group 50 farmers grew three crops most frequently beans pepper and cabbageFinally in the last group among the 25 farmers with five crops potato pepper beanscabbage and Ligularia fischeri dominated However because Ligularia fischeri was relativelynewly introduced to consumers the price data contained large and regularly occurring gaps(Supplementary Table ST1) Therefore SSA could not be carried out for this crop As analternative we have included radish in the five-crop portfolio as the sixth most frequentlychosen crop by farmers who grew five crops We calculated the relative proportions of thesethree or five main crops and composed the empirical crop portfolios as follows

(1) Single crop farming six major crops (100)

(2) Three-crop portfolio beans (350) pepper (325) and cabbage (325)

(3) Five-crop portfolio potato (290) pepper (277) beans (174) cabbage (144)and radish (115)

32 Crop price fluctuations

321 Single crops

Figure 2 shows the variabilities of crop price fluctuations among six main crops in theGangwon Province of South Korea The visual comparison of price data showed that the riceprice was extremely stable compared to any other analysed crops during the study period(Figure 2 and Supplementary Figure SF3 for non-normalised price data) Because rice is themost important cereal crop in South Korea (Korea Rural Economic Institute 2015) severalpolicy instruments such as government buffer stock schemes and direct payments were usedto stabilise the rice price (Park et al 2010) Even though the price for beans was alsorelatively stable a sharp increase was registered in 2004 The price for beans in South Koreais highly dependent on foreign trade and is directly influenced by the global market (OECD

11

Year

Nor

mal

ized

pric

e (K

RW

kg)

minus40

000

2000

6000

1996 1998 2000 2002 2004 2006 2008 2010 2012

ricebeans

potatoradisch

cabbagepepper

Ligularia fischeri

Year

Nor

mal

ized

yie

ld (

ton

ha)

minus15

minus10

minus5

05

1015

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

rice beans potato radisch cabbage pepper

Figure 2 The variability of the normalised crop price (left) and the normalised yield (right) over the analysedperiod The respective mean was subtracted from each time series

2008) Because the US soybean crop yield in 2003 has been the lowest since 1992 theprice in 2004 increased dramatically (USDA 2007) Similarly a large price rise for cabbagewas observed in 2010 although for a different reason (Supplementary Figure SF3 (e) andFigure 2) Due to bad weather in 2010 the supply of cabbage did not meet the demand(Kwon 2012) In comparison to rice and beans the prices for pepper and Ligularia fischerifluctuated strongly

Figure 3 shows the results of the SSA decomposition of the crop prices We consideredfour time scales of fluctuations and evaluated their importance by the ratio of the eigenvalues(cf numbers in parenthesis in Figure 3) These numbers show how much each time scalecontributes to the reconstruction of the original time series We associate the periodicitiesof 24 months and more with a trend and those of 6ndash24 months with seasonal fluctuationsThe third (3ndash59 months) and the fourth (lt 29 months) time scales are however too shortto be interpreted

The prices for rice and beans showed a large contribution of the trend (701 and 546respectively) and a minor one on the smallest time scale (26 and 4 respectively) Thisconfirms the visual impression of stability in Figure 2 Except for rice the crop price datashowed considerable seasonal patterns with the ratio of eigenvalues exceeding 30 Radishand pepper exhibited an especially strong seasonal fluctuation namely 436 and 426respectively Compared to rice and beans cabbage and pepper had a substantial contributionto fluctuations at the smallest time scale (124 and 175 respectively)

322 Crop portfolios

The thee-crop portfolio consisted of beans (35) pepper (325) and cabbage (325)(Figure 4 (a)) The SSA of single crops (Figure 3) showed that the bean price was one ofthe least fluctuating and dominated by the trend whilst pepper and cabbage exhibited alarge seasonal variation The combination of them increased the contribution of the trend(compared to pepper) and decreased the importance of seasonal fluctuations (compared topepper and cabbage) (Figure 4 (a)) However in comparison to the trend-dominated beanprice the fluctuations on all but the largest time scale (trend) increased

The five-crop portfolio included potato (29) pepper (277) beans (174) cabbage(144) and radish (115) (Figure 4 (b)) Compared to the trend-dominated bean price

12

1600

1800

2000

original data gt 24 months (701)(a)

Time

minus50

50

6minus24 months (183)

Time

minus20

20

3minus59 months (89)

Time

minus10

515lt 29 months (26)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

5000

8000

original data gt 24 months (546)(b)

Time

minus20

0020

006minus24 months (303)

Time

minus20

040

0

3minus59 months (111)

Time

minus20

00

200

lt 29 months (4)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

050

015

0025

00

original data gt 24 months (314)(c)

Time

minus40

040

06minus24 months (357)

Time

minus30

030

0 3minus59 months (237)

Time

minus10

020

0lt 29 months (92)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500 original data gt 24 months (238)(d)

Time

minus20

040

06minus24 months (436)

Time

minus20

020

0 3minus59 months (232)

Time

minus10

010

0lt 29 months (95)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500

original data gt 24 months (252)(e)

Time

minus50

050

0

6minus24 months (39)

Time

minus20

020

0 3minus59 months (234)

Time

minus20

020

0

lt 29 months (124)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

6000

1200

0 original data gt 24 months (122)(f)

Time

minus40

0040

006minus24 months (426)

Time

minus20

0020

00 3minus59 months (277)

Time

minus20

0020

00lt 29 months (175)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 3 SSA decomposition of the crop prices (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper Four groups of fluctuation were considered larger than 24 months (trend) 6ndash24 months (sea-sonality) 3ndash59 months smaller than 29 months The number in parenthesis shows the ratio of eigenvaluesThe trend component contains the mean the others show the variability around it

13

1000

3000

5000

original data gt 24 months (239)(a)

Time

minus20

0020

006minus24 months (352)

Time

minus50

050

0 3minus59 months (259)

Timeminus

400

400lt 29 months (15)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

1000

3000

5000

original data gt 24 months (204)(b)

Time

minus20

0020

006minus24 months (408)

Time

minus50

050

0 3minus59 months (236)

Time

minus40

040

0lt 29 months (152)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 4 SSA decomposition of the portfolio prices (a) three-crops portfolio (beans (350) pepper (325)and cabbage (325)) and (b) five-crops portfolio (potato (29) pepper (277) beans (174) cabbage(144) and radish (115))For both portfolio four periods of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it

the contribution of the trend decreased from 546 to 204 Additionally the contributionof the seasonal fluctuation remained comparable to the other crops that have a strong sea-sonal pattern In summary the results of SSA decomposition were similar to the portfoliocomposed of three crops Indeed the summed contributions of the larger time scales (trendand seasonality) as well as those on the smaller time scales differed only slightly

33 Crop yield fluctuations

An in-depth analysis of seasonality was not possible because the time series of yieldconsisted of annual measurements Therefore we only extracted the trend and calculatedthe dominant frequency of the remaining periodicities (Figure 5) The result of SSA showedthat the contribution of the trend varied from 333 to 665 Accordingly the importanceof periodicities ranged from 335 to 667 Their dominant frequency covered 25 years to107 years

In general crop yield had an upwards trend during the analysed period except forradish and cabbage (Figure 5) Four of the six analysed crops namely rice beans potatoand pepper showed increasing trends in the yields In contrast the yield of radish andcabbage had decreased during the 23-year analysed period There were more negative thanpositive extreme values outside the range of the standard deviation of the trend Additionallythe amplitude of negative values was often larger than that of positive values (Figure 5)Interestingly large negative values occurred in different years for different crops In 1980and 1993 for example the rice yield decreased sharply whereas there was a relatively high

14

23

45

6

original data trend (457)(a)

Time

minus2

01

2

25 years (543)

1965 1975 1985 1995 2005

Yie

ld (

ton

ha)

Year

10

12

14

16

18

20

original data trend (333)(b)

Time

minus0

30

00

3

4 years (667)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

1015

2025

3035

40 original data trend (424)(c)

Time

minus10

0527 years (576)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3034

3842 original data trend (349)

(d)

Time

minus6

04

8

46 years (651)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3540

4550

5560 original data trend (344)

(e)

Time

minus10

0523 years (656)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

24

68

1012 original data trend (665)

(f)

Time

minus3

minus1

13

107 years (335)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

Figure 5 SSA decomposition of the crop yield (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper The number in parenthesis shows the ratio of eigenvalues The trend component contains themean the others show the variability around it The yellow area shows plusmn standard deviation around thetrend component Note that the time scale is years and not months as for the price data Fluctuations withperiods of 23 years and 16 years (trend) were chosen for rice and the other crops respectively

15

Year

Rea

l Rev

enue

(M

illio

n K

RW

haminus1

year

minus1)

020

4060

1996 1998 2000 2002 2004 2006 2008 2010

ricebeans

potatoradisch

cabbagepepper

threeminuscrop portfoliofiveminuscrop portfolio

Figure 6 Real revenue for single crops and the empirical crop portfolios

yield in potato in the same year In 1996 the radish yield was very low and the rice yieldmoderately high (See Figure 5 and Supplementary Figure SF4)

The sharp drops of yield often followed damages caused by unusual weather eventsEspecially in 1980 the rice yield reached only 587 of the target yield of South Koreadue to low temperature (Park et al 2010) In 1987 and 2010 radish and cabbage werealso influenced by bad weather (Kwon 2012) Frequent rain and lack of sunlight duringseeding period harmed stabilising seeds (Han and Kim 2010) In addition the yield ofradish and cabbage has declined as the consumption decreases and imports increase (KoreaRural Economic Institute 2015) Actually the import of cabbage has increased since 2003and westernised eating habits of South Koreans has decreased its consumption by 2 peryear since 2002 (Korea Rural Economic Institute 2015)

34 Risk adjusted revenue

The revenue and the Sharpe ratio for each crop portfolio are depicted in Figure 6 andTable 4 The Sharpe ratio is often used to assess the portfolio performance (Blank 1990Roche and McQuinn 2004 Gaydon et al 2012) For example Roche and McQuinn (2004)calculated the Sharpe ratio for the farm land allocation portfolio for grains and Gaydon et al(2012) used it for comparing water management options and their contribution to the farmincome

Figure 6 shows the temporal change of the real revenue of single crops and three-and five-crop portfolios Large differences between the six main crops were observed Rice and beansshowed a stable but the smallest and decreasing revenue compared to the other crops overthe analysed period Pepper showed the highest revenue with the highest standard deviation(Table 4) In the portfolio the mean revenue doubled or tripled and the standard deviationincreased with the number of crops compared to rice and bean single crop farming Althoughthe mean revenue of the crop portfolios was smaller compared to potato and pepper itsstandard deviation decreased The difference between the three- and the five-crop portfoliosin mean and standard deviation was only minor

16

Table 4 Risks adjusted revenue for the analysed period from 1996 to 2011

Crop selection Mean (million KRW) SD Sharpe ratio

Single croprice 1085 173 627

beans 596 175 340potato 3092 770 401radish 1476 298 495

cabbage 2288 435 526pepper 3294 1420 232

three-crop portfolio 2023 532 380five-crop portfolio 2412 560 430

4 Discussion

An advantage of decomposing the time series is that we can not only identify the mostfluctuating crop over time but also quantify different components of fluctuations in eachcrop Fluctuations on larger time scales (trend and seasonality) are easier for farmers toface than short-time variations which are more difficult to address in the planning processIn order to distinguish four time scales of fluctuations in each crop selection we calculatedthe ratio of eigenvalue for each time scale The ratio of eigenvalue stands for the quality ofthe reconstruction of the original time series by a certain component The larger this ratiothe more important the component will be for the reconstruction Among four time scalesthe first and the second scales can be interpreted as trend and seasonality respectively thethird and the fourth scales however were too short to be identified

Farmersrsquo decision on which crop to grow how to allocate the land to grow multiple cropsand when to harvest and sell them plays a crucial role to secure their revenue (Fafchamps1992 Kantanantha et al 2010 Klasen et al 2013) Our result showed that each crop had adifferent fluctuation pattern that highly influenced the farm revenue depending on farmersrsquocrop selection The sum of the first two ratios of eigenvalues for crop price ranged from 548(pepper) to 884 (rice) The larger the contribution of trend and seasonality the less short-time variability is contained in the data Four of the six analysed crops contained notableseasonal patterns The SSA of the three- and the five-crop portfolios also revealed thatimportant seasonal variation still remained in the monthly price data Therefore seasonalityprobably has an important impact on farmersrsquo decisions regarding the times for harvestingor marketing of their crops

The risk adjusted revenue calculated with the Sharpe ratio allows us to compare how muchrevenue standardised per 1 of revenue can be guaranteed for farmers in each crop selectionThe combination of these methods provides more information to support farmersrsquo decision oncrop selection Although the results of SSA and the Sharpe ratio showed that rice and beanfarming were the most stable they provided the lowest revenue The revenue of the three-and the five-crop portfolios was more than two times larger than in rice farming howeverat the same time the standard deviation tripled (Table 4) It indicates that the diversified

17

Time

Pric

e (U

SDto

n)

500

1000

1500

2000

1996 1998 2000 2002 2004 2006 2008 2010 2012

Korean domestic rice price World rice price

200

600

1000 original data gt 24 months (684)

Time

minus10

050

6minus24 months (154)

Time

minus10

00

100

3minus59 months (107)

Time

minus40

040

lt 29 months (54)

1991 1997 2003 2009 2015

Pric

e (U

SD

ton)

Year

Figure 7 Korean domestic rice price converted in USDton and world rice price in USDton (left) SSAdecomposition of the world rice price (right) Four groups of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it The world rice data was Thailand nominal price quote obtained from the World BankGlobal Economic Monitor (GEM) Commodities The exchange rate from Korean Won to USD for each yearwas obtained from the World Bank World Development Indicators

farming could support larger revenue This is in accordance with the study by Bhattacharyya(2008) who showed that a rice dominated farming system in India was changed to high-valuecrops for larger revenue Furthermore an analysis in Argentina showed that diversifiedfarming increased the mean return on capital with a lower coefficient of variation (Pacın andOesterheld 2014) Hence the multiple crop farming may be a means of enhancing revenue(Ali et al 2004 Winters et al 2006 Pacın and Oesterheld 2014 Rahman and Kazal 2015)However the diversification took place slowly due to agricultural subsidies concentrated ona certain crop such as rice in India (Bhattacharyya 2008) This might also be the case inSouth Korea

To examine the artificial stability of the rice price in South Korea we compared thedomestic rice price with the world rice price in USD (Figure 7) As the exchange rate variesbetween years the domestic rice price converted in USD fluctuated more compared to theone in KRW We refer to the SSA result of the rice price in KRW to keep consistency unlessmentioned While the world rice price increased drastically in 2008 as a result of the oilcrisis (Figure 7 right) the Korean domestic price was not affected by it and remained stable(Figure 3 (a)) Overall rice price in the global market fluctuates more than in the SouthKorean domestic market (Baffes and Cosic 2013) Furthermore the Korean domestic priceis more than double or triple the world price ndash the result of a substantial governmentalsupport (Figure 7 left)

South Korea used to have a higher protection for domestic rice farming mainly throughtariff and non-tariff barriers in comparison to other OECD countries (Aksoy 2005) Amongother conventional crops Korean subsidy policy focuses particularly on rice farming by sup-

18

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

Table 3 Number of farmers cultivating the eight main crops in the watershed of the Soyang Lake in theGangwon Province

Rank Crop Number of farmers

1 Pepper 1332 Potato 1163 Beans 904 Ligularia fischeri 645 Rice 596 Radish 527 Cabbage 427 Maize 42

as they were the majorities in each group Then we looked at the most selected crops by eachgroup of farmers Rice was the most frequently cultivated crop by farmers who cultivated asingle crop However as rice is the main staple grain in South Korea rice is highly subsidisedby the government (Korea Rural Economic Institute 2015) which might lead to differentprice conditions compared to the other single crops Therefore we decided not to have riceas a representative crop for the single crop farming but compared all six chosen crops Inthe second group 50 farmers grew three crops most frequently beans pepper and cabbageFinally in the last group among the 25 farmers with five crops potato pepper beanscabbage and Ligularia fischeri dominated However because Ligularia fischeri was relativelynewly introduced to consumers the price data contained large and regularly occurring gaps(Supplementary Table ST1) Therefore SSA could not be carried out for this crop As analternative we have included radish in the five-crop portfolio as the sixth most frequentlychosen crop by farmers who grew five crops We calculated the relative proportions of thesethree or five main crops and composed the empirical crop portfolios as follows

(1) Single crop farming six major crops (100)

(2) Three-crop portfolio beans (350) pepper (325) and cabbage (325)

(3) Five-crop portfolio potato (290) pepper (277) beans (174) cabbage (144)and radish (115)

32 Crop price fluctuations

321 Single crops

Figure 2 shows the variabilities of crop price fluctuations among six main crops in theGangwon Province of South Korea The visual comparison of price data showed that the riceprice was extremely stable compared to any other analysed crops during the study period(Figure 2 and Supplementary Figure SF3 for non-normalised price data) Because rice is themost important cereal crop in South Korea (Korea Rural Economic Institute 2015) severalpolicy instruments such as government buffer stock schemes and direct payments were usedto stabilise the rice price (Park et al 2010) Even though the price for beans was alsorelatively stable a sharp increase was registered in 2004 The price for beans in South Koreais highly dependent on foreign trade and is directly influenced by the global market (OECD

11

Year

Nor

mal

ized

pric

e (K

RW

kg)

minus40

000

2000

6000

1996 1998 2000 2002 2004 2006 2008 2010 2012

ricebeans

potatoradisch

cabbagepepper

Ligularia fischeri

Year

Nor

mal

ized

yie

ld (

ton

ha)

minus15

minus10

minus5

05

1015

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

rice beans potato radisch cabbage pepper

Figure 2 The variability of the normalised crop price (left) and the normalised yield (right) over the analysedperiod The respective mean was subtracted from each time series

2008) Because the US soybean crop yield in 2003 has been the lowest since 1992 theprice in 2004 increased dramatically (USDA 2007) Similarly a large price rise for cabbagewas observed in 2010 although for a different reason (Supplementary Figure SF3 (e) andFigure 2) Due to bad weather in 2010 the supply of cabbage did not meet the demand(Kwon 2012) In comparison to rice and beans the prices for pepper and Ligularia fischerifluctuated strongly

Figure 3 shows the results of the SSA decomposition of the crop prices We consideredfour time scales of fluctuations and evaluated their importance by the ratio of the eigenvalues(cf numbers in parenthesis in Figure 3) These numbers show how much each time scalecontributes to the reconstruction of the original time series We associate the periodicitiesof 24 months and more with a trend and those of 6ndash24 months with seasonal fluctuationsThe third (3ndash59 months) and the fourth (lt 29 months) time scales are however too shortto be interpreted

The prices for rice and beans showed a large contribution of the trend (701 and 546respectively) and a minor one on the smallest time scale (26 and 4 respectively) Thisconfirms the visual impression of stability in Figure 2 Except for rice the crop price datashowed considerable seasonal patterns with the ratio of eigenvalues exceeding 30 Radishand pepper exhibited an especially strong seasonal fluctuation namely 436 and 426respectively Compared to rice and beans cabbage and pepper had a substantial contributionto fluctuations at the smallest time scale (124 and 175 respectively)

322 Crop portfolios

The thee-crop portfolio consisted of beans (35) pepper (325) and cabbage (325)(Figure 4 (a)) The SSA of single crops (Figure 3) showed that the bean price was one ofthe least fluctuating and dominated by the trend whilst pepper and cabbage exhibited alarge seasonal variation The combination of them increased the contribution of the trend(compared to pepper) and decreased the importance of seasonal fluctuations (compared topepper and cabbage) (Figure 4 (a)) However in comparison to the trend-dominated beanprice the fluctuations on all but the largest time scale (trend) increased

The five-crop portfolio included potato (29) pepper (277) beans (174) cabbage(144) and radish (115) (Figure 4 (b)) Compared to the trend-dominated bean price

12

1600

1800

2000

original data gt 24 months (701)(a)

Time

minus50

50

6minus24 months (183)

Time

minus20

20

3minus59 months (89)

Time

minus10

515lt 29 months (26)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

5000

8000

original data gt 24 months (546)(b)

Time

minus20

0020

006minus24 months (303)

Time

minus20

040

0

3minus59 months (111)

Time

minus20

00

200

lt 29 months (4)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

050

015

0025

00

original data gt 24 months (314)(c)

Time

minus40

040

06minus24 months (357)

Time

minus30

030

0 3minus59 months (237)

Time

minus10

020

0lt 29 months (92)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500 original data gt 24 months (238)(d)

Time

minus20

040

06minus24 months (436)

Time

minus20

020

0 3minus59 months (232)

Time

minus10

010

0lt 29 months (95)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500

original data gt 24 months (252)(e)

Time

minus50

050

0

6minus24 months (39)

Time

minus20

020

0 3minus59 months (234)

Time

minus20

020

0

lt 29 months (124)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

6000

1200

0 original data gt 24 months (122)(f)

Time

minus40

0040

006minus24 months (426)

Time

minus20

0020

00 3minus59 months (277)

Time

minus20

0020

00lt 29 months (175)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 3 SSA decomposition of the crop prices (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper Four groups of fluctuation were considered larger than 24 months (trend) 6ndash24 months (sea-sonality) 3ndash59 months smaller than 29 months The number in parenthesis shows the ratio of eigenvaluesThe trend component contains the mean the others show the variability around it

13

1000

3000

5000

original data gt 24 months (239)(a)

Time

minus20

0020

006minus24 months (352)

Time

minus50

050

0 3minus59 months (259)

Timeminus

400

400lt 29 months (15)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

1000

3000

5000

original data gt 24 months (204)(b)

Time

minus20

0020

006minus24 months (408)

Time

minus50

050

0 3minus59 months (236)

Time

minus40

040

0lt 29 months (152)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 4 SSA decomposition of the portfolio prices (a) three-crops portfolio (beans (350) pepper (325)and cabbage (325)) and (b) five-crops portfolio (potato (29) pepper (277) beans (174) cabbage(144) and radish (115))For both portfolio four periods of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it

the contribution of the trend decreased from 546 to 204 Additionally the contributionof the seasonal fluctuation remained comparable to the other crops that have a strong sea-sonal pattern In summary the results of SSA decomposition were similar to the portfoliocomposed of three crops Indeed the summed contributions of the larger time scales (trendand seasonality) as well as those on the smaller time scales differed only slightly

33 Crop yield fluctuations

An in-depth analysis of seasonality was not possible because the time series of yieldconsisted of annual measurements Therefore we only extracted the trend and calculatedthe dominant frequency of the remaining periodicities (Figure 5) The result of SSA showedthat the contribution of the trend varied from 333 to 665 Accordingly the importanceof periodicities ranged from 335 to 667 Their dominant frequency covered 25 years to107 years

In general crop yield had an upwards trend during the analysed period except forradish and cabbage (Figure 5) Four of the six analysed crops namely rice beans potatoand pepper showed increasing trends in the yields In contrast the yield of radish andcabbage had decreased during the 23-year analysed period There were more negative thanpositive extreme values outside the range of the standard deviation of the trend Additionallythe amplitude of negative values was often larger than that of positive values (Figure 5)Interestingly large negative values occurred in different years for different crops In 1980and 1993 for example the rice yield decreased sharply whereas there was a relatively high

14

23

45

6

original data trend (457)(a)

Time

minus2

01

2

25 years (543)

1965 1975 1985 1995 2005

Yie

ld (

ton

ha)

Year

10

12

14

16

18

20

original data trend (333)(b)

Time

minus0

30

00

3

4 years (667)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

1015

2025

3035

40 original data trend (424)(c)

Time

minus10

0527 years (576)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3034

3842 original data trend (349)

(d)

Time

minus6

04

8

46 years (651)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3540

4550

5560 original data trend (344)

(e)

Time

minus10

0523 years (656)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

24

68

1012 original data trend (665)

(f)

Time

minus3

minus1

13

107 years (335)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

Figure 5 SSA decomposition of the crop yield (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper The number in parenthesis shows the ratio of eigenvalues The trend component contains themean the others show the variability around it The yellow area shows plusmn standard deviation around thetrend component Note that the time scale is years and not months as for the price data Fluctuations withperiods of 23 years and 16 years (trend) were chosen for rice and the other crops respectively

15

Year

Rea

l Rev

enue

(M

illio

n K

RW

haminus1

year

minus1)

020

4060

1996 1998 2000 2002 2004 2006 2008 2010

ricebeans

potatoradisch

cabbagepepper

threeminuscrop portfoliofiveminuscrop portfolio

Figure 6 Real revenue for single crops and the empirical crop portfolios

yield in potato in the same year In 1996 the radish yield was very low and the rice yieldmoderately high (See Figure 5 and Supplementary Figure SF4)

The sharp drops of yield often followed damages caused by unusual weather eventsEspecially in 1980 the rice yield reached only 587 of the target yield of South Koreadue to low temperature (Park et al 2010) In 1987 and 2010 radish and cabbage werealso influenced by bad weather (Kwon 2012) Frequent rain and lack of sunlight duringseeding period harmed stabilising seeds (Han and Kim 2010) In addition the yield ofradish and cabbage has declined as the consumption decreases and imports increase (KoreaRural Economic Institute 2015) Actually the import of cabbage has increased since 2003and westernised eating habits of South Koreans has decreased its consumption by 2 peryear since 2002 (Korea Rural Economic Institute 2015)

34 Risk adjusted revenue

The revenue and the Sharpe ratio for each crop portfolio are depicted in Figure 6 andTable 4 The Sharpe ratio is often used to assess the portfolio performance (Blank 1990Roche and McQuinn 2004 Gaydon et al 2012) For example Roche and McQuinn (2004)calculated the Sharpe ratio for the farm land allocation portfolio for grains and Gaydon et al(2012) used it for comparing water management options and their contribution to the farmincome

Figure 6 shows the temporal change of the real revenue of single crops and three-and five-crop portfolios Large differences between the six main crops were observed Rice and beansshowed a stable but the smallest and decreasing revenue compared to the other crops overthe analysed period Pepper showed the highest revenue with the highest standard deviation(Table 4) In the portfolio the mean revenue doubled or tripled and the standard deviationincreased with the number of crops compared to rice and bean single crop farming Althoughthe mean revenue of the crop portfolios was smaller compared to potato and pepper itsstandard deviation decreased The difference between the three- and the five-crop portfoliosin mean and standard deviation was only minor

16

Table 4 Risks adjusted revenue for the analysed period from 1996 to 2011

Crop selection Mean (million KRW) SD Sharpe ratio

Single croprice 1085 173 627

beans 596 175 340potato 3092 770 401radish 1476 298 495

cabbage 2288 435 526pepper 3294 1420 232

three-crop portfolio 2023 532 380five-crop portfolio 2412 560 430

4 Discussion

An advantage of decomposing the time series is that we can not only identify the mostfluctuating crop over time but also quantify different components of fluctuations in eachcrop Fluctuations on larger time scales (trend and seasonality) are easier for farmers toface than short-time variations which are more difficult to address in the planning processIn order to distinguish four time scales of fluctuations in each crop selection we calculatedthe ratio of eigenvalue for each time scale The ratio of eigenvalue stands for the quality ofthe reconstruction of the original time series by a certain component The larger this ratiothe more important the component will be for the reconstruction Among four time scalesthe first and the second scales can be interpreted as trend and seasonality respectively thethird and the fourth scales however were too short to be identified

Farmersrsquo decision on which crop to grow how to allocate the land to grow multiple cropsand when to harvest and sell them plays a crucial role to secure their revenue (Fafchamps1992 Kantanantha et al 2010 Klasen et al 2013) Our result showed that each crop had adifferent fluctuation pattern that highly influenced the farm revenue depending on farmersrsquocrop selection The sum of the first two ratios of eigenvalues for crop price ranged from 548(pepper) to 884 (rice) The larger the contribution of trend and seasonality the less short-time variability is contained in the data Four of the six analysed crops contained notableseasonal patterns The SSA of the three- and the five-crop portfolios also revealed thatimportant seasonal variation still remained in the monthly price data Therefore seasonalityprobably has an important impact on farmersrsquo decisions regarding the times for harvestingor marketing of their crops

The risk adjusted revenue calculated with the Sharpe ratio allows us to compare how muchrevenue standardised per 1 of revenue can be guaranteed for farmers in each crop selectionThe combination of these methods provides more information to support farmersrsquo decision oncrop selection Although the results of SSA and the Sharpe ratio showed that rice and beanfarming were the most stable they provided the lowest revenue The revenue of the three-and the five-crop portfolios was more than two times larger than in rice farming howeverat the same time the standard deviation tripled (Table 4) It indicates that the diversified

17

Time

Pric

e (U

SDto

n)

500

1000

1500

2000

1996 1998 2000 2002 2004 2006 2008 2010 2012

Korean domestic rice price World rice price

200

600

1000 original data gt 24 months (684)

Time

minus10

050

6minus24 months (154)

Time

minus10

00

100

3minus59 months (107)

Time

minus40

040

lt 29 months (54)

1991 1997 2003 2009 2015

Pric

e (U

SD

ton)

Year

Figure 7 Korean domestic rice price converted in USDton and world rice price in USDton (left) SSAdecomposition of the world rice price (right) Four groups of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it The world rice data was Thailand nominal price quote obtained from the World BankGlobal Economic Monitor (GEM) Commodities The exchange rate from Korean Won to USD for each yearwas obtained from the World Bank World Development Indicators

farming could support larger revenue This is in accordance with the study by Bhattacharyya(2008) who showed that a rice dominated farming system in India was changed to high-valuecrops for larger revenue Furthermore an analysis in Argentina showed that diversifiedfarming increased the mean return on capital with a lower coefficient of variation (Pacın andOesterheld 2014) Hence the multiple crop farming may be a means of enhancing revenue(Ali et al 2004 Winters et al 2006 Pacın and Oesterheld 2014 Rahman and Kazal 2015)However the diversification took place slowly due to agricultural subsidies concentrated ona certain crop such as rice in India (Bhattacharyya 2008) This might also be the case inSouth Korea

To examine the artificial stability of the rice price in South Korea we compared thedomestic rice price with the world rice price in USD (Figure 7) As the exchange rate variesbetween years the domestic rice price converted in USD fluctuated more compared to theone in KRW We refer to the SSA result of the rice price in KRW to keep consistency unlessmentioned While the world rice price increased drastically in 2008 as a result of the oilcrisis (Figure 7 right) the Korean domestic price was not affected by it and remained stable(Figure 3 (a)) Overall rice price in the global market fluctuates more than in the SouthKorean domestic market (Baffes and Cosic 2013) Furthermore the Korean domestic priceis more than double or triple the world price ndash the result of a substantial governmentalsupport (Figure 7 left)

South Korea used to have a higher protection for domestic rice farming mainly throughtariff and non-tariff barriers in comparison to other OECD countries (Aksoy 2005) Amongother conventional crops Korean subsidy policy focuses particularly on rice farming by sup-

18

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

Year

Nor

mal

ized

pric

e (K

RW

kg)

minus40

000

2000

6000

1996 1998 2000 2002 2004 2006 2008 2010 2012

ricebeans

potatoradisch

cabbagepepper

Ligularia fischeri

Year

Nor

mal

ized

yie

ld (

ton

ha)

minus15

minus10

minus5

05

1015

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

rice beans potato radisch cabbage pepper

Figure 2 The variability of the normalised crop price (left) and the normalised yield (right) over the analysedperiod The respective mean was subtracted from each time series

2008) Because the US soybean crop yield in 2003 has been the lowest since 1992 theprice in 2004 increased dramatically (USDA 2007) Similarly a large price rise for cabbagewas observed in 2010 although for a different reason (Supplementary Figure SF3 (e) andFigure 2) Due to bad weather in 2010 the supply of cabbage did not meet the demand(Kwon 2012) In comparison to rice and beans the prices for pepper and Ligularia fischerifluctuated strongly

Figure 3 shows the results of the SSA decomposition of the crop prices We consideredfour time scales of fluctuations and evaluated their importance by the ratio of the eigenvalues(cf numbers in parenthesis in Figure 3) These numbers show how much each time scalecontributes to the reconstruction of the original time series We associate the periodicitiesof 24 months and more with a trend and those of 6ndash24 months with seasonal fluctuationsThe third (3ndash59 months) and the fourth (lt 29 months) time scales are however too shortto be interpreted

The prices for rice and beans showed a large contribution of the trend (701 and 546respectively) and a minor one on the smallest time scale (26 and 4 respectively) Thisconfirms the visual impression of stability in Figure 2 Except for rice the crop price datashowed considerable seasonal patterns with the ratio of eigenvalues exceeding 30 Radishand pepper exhibited an especially strong seasonal fluctuation namely 436 and 426respectively Compared to rice and beans cabbage and pepper had a substantial contributionto fluctuations at the smallest time scale (124 and 175 respectively)

322 Crop portfolios

The thee-crop portfolio consisted of beans (35) pepper (325) and cabbage (325)(Figure 4 (a)) The SSA of single crops (Figure 3) showed that the bean price was one ofthe least fluctuating and dominated by the trend whilst pepper and cabbage exhibited alarge seasonal variation The combination of them increased the contribution of the trend(compared to pepper) and decreased the importance of seasonal fluctuations (compared topepper and cabbage) (Figure 4 (a)) However in comparison to the trend-dominated beanprice the fluctuations on all but the largest time scale (trend) increased

The five-crop portfolio included potato (29) pepper (277) beans (174) cabbage(144) and radish (115) (Figure 4 (b)) Compared to the trend-dominated bean price

12

1600

1800

2000

original data gt 24 months (701)(a)

Time

minus50

50

6minus24 months (183)

Time

minus20

20

3minus59 months (89)

Time

minus10

515lt 29 months (26)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

5000

8000

original data gt 24 months (546)(b)

Time

minus20

0020

006minus24 months (303)

Time

minus20

040

0

3minus59 months (111)

Time

minus20

00

200

lt 29 months (4)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

050

015

0025

00

original data gt 24 months (314)(c)

Time

minus40

040

06minus24 months (357)

Time

minus30

030

0 3minus59 months (237)

Time

minus10

020

0lt 29 months (92)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500 original data gt 24 months (238)(d)

Time

minus20

040

06minus24 months (436)

Time

minus20

020

0 3minus59 months (232)

Time

minus10

010

0lt 29 months (95)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500

original data gt 24 months (252)(e)

Time

minus50

050

0

6minus24 months (39)

Time

minus20

020

0 3minus59 months (234)

Time

minus20

020

0

lt 29 months (124)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

6000

1200

0 original data gt 24 months (122)(f)

Time

minus40

0040

006minus24 months (426)

Time

minus20

0020

00 3minus59 months (277)

Time

minus20

0020

00lt 29 months (175)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 3 SSA decomposition of the crop prices (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper Four groups of fluctuation were considered larger than 24 months (trend) 6ndash24 months (sea-sonality) 3ndash59 months smaller than 29 months The number in parenthesis shows the ratio of eigenvaluesThe trend component contains the mean the others show the variability around it

13

1000

3000

5000

original data gt 24 months (239)(a)

Time

minus20

0020

006minus24 months (352)

Time

minus50

050

0 3minus59 months (259)

Timeminus

400

400lt 29 months (15)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

1000

3000

5000

original data gt 24 months (204)(b)

Time

minus20

0020

006minus24 months (408)

Time

minus50

050

0 3minus59 months (236)

Time

minus40

040

0lt 29 months (152)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 4 SSA decomposition of the portfolio prices (a) three-crops portfolio (beans (350) pepper (325)and cabbage (325)) and (b) five-crops portfolio (potato (29) pepper (277) beans (174) cabbage(144) and radish (115))For both portfolio four periods of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it

the contribution of the trend decreased from 546 to 204 Additionally the contributionof the seasonal fluctuation remained comparable to the other crops that have a strong sea-sonal pattern In summary the results of SSA decomposition were similar to the portfoliocomposed of three crops Indeed the summed contributions of the larger time scales (trendand seasonality) as well as those on the smaller time scales differed only slightly

33 Crop yield fluctuations

An in-depth analysis of seasonality was not possible because the time series of yieldconsisted of annual measurements Therefore we only extracted the trend and calculatedthe dominant frequency of the remaining periodicities (Figure 5) The result of SSA showedthat the contribution of the trend varied from 333 to 665 Accordingly the importanceof periodicities ranged from 335 to 667 Their dominant frequency covered 25 years to107 years

In general crop yield had an upwards trend during the analysed period except forradish and cabbage (Figure 5) Four of the six analysed crops namely rice beans potatoand pepper showed increasing trends in the yields In contrast the yield of radish andcabbage had decreased during the 23-year analysed period There were more negative thanpositive extreme values outside the range of the standard deviation of the trend Additionallythe amplitude of negative values was often larger than that of positive values (Figure 5)Interestingly large negative values occurred in different years for different crops In 1980and 1993 for example the rice yield decreased sharply whereas there was a relatively high

14

23

45

6

original data trend (457)(a)

Time

minus2

01

2

25 years (543)

1965 1975 1985 1995 2005

Yie

ld (

ton

ha)

Year

10

12

14

16

18

20

original data trend (333)(b)

Time

minus0

30

00

3

4 years (667)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

1015

2025

3035

40 original data trend (424)(c)

Time

minus10

0527 years (576)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3034

3842 original data trend (349)

(d)

Time

minus6

04

8

46 years (651)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3540

4550

5560 original data trend (344)

(e)

Time

minus10

0523 years (656)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

24

68

1012 original data trend (665)

(f)

Time

minus3

minus1

13

107 years (335)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

Figure 5 SSA decomposition of the crop yield (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper The number in parenthesis shows the ratio of eigenvalues The trend component contains themean the others show the variability around it The yellow area shows plusmn standard deviation around thetrend component Note that the time scale is years and not months as for the price data Fluctuations withperiods of 23 years and 16 years (trend) were chosen for rice and the other crops respectively

15

Year

Rea

l Rev

enue

(M

illio

n K

RW

haminus1

year

minus1)

020

4060

1996 1998 2000 2002 2004 2006 2008 2010

ricebeans

potatoradisch

cabbagepepper

threeminuscrop portfoliofiveminuscrop portfolio

Figure 6 Real revenue for single crops and the empirical crop portfolios

yield in potato in the same year In 1996 the radish yield was very low and the rice yieldmoderately high (See Figure 5 and Supplementary Figure SF4)

The sharp drops of yield often followed damages caused by unusual weather eventsEspecially in 1980 the rice yield reached only 587 of the target yield of South Koreadue to low temperature (Park et al 2010) In 1987 and 2010 radish and cabbage werealso influenced by bad weather (Kwon 2012) Frequent rain and lack of sunlight duringseeding period harmed stabilising seeds (Han and Kim 2010) In addition the yield ofradish and cabbage has declined as the consumption decreases and imports increase (KoreaRural Economic Institute 2015) Actually the import of cabbage has increased since 2003and westernised eating habits of South Koreans has decreased its consumption by 2 peryear since 2002 (Korea Rural Economic Institute 2015)

34 Risk adjusted revenue

The revenue and the Sharpe ratio for each crop portfolio are depicted in Figure 6 andTable 4 The Sharpe ratio is often used to assess the portfolio performance (Blank 1990Roche and McQuinn 2004 Gaydon et al 2012) For example Roche and McQuinn (2004)calculated the Sharpe ratio for the farm land allocation portfolio for grains and Gaydon et al(2012) used it for comparing water management options and their contribution to the farmincome

Figure 6 shows the temporal change of the real revenue of single crops and three-and five-crop portfolios Large differences between the six main crops were observed Rice and beansshowed a stable but the smallest and decreasing revenue compared to the other crops overthe analysed period Pepper showed the highest revenue with the highest standard deviation(Table 4) In the portfolio the mean revenue doubled or tripled and the standard deviationincreased with the number of crops compared to rice and bean single crop farming Althoughthe mean revenue of the crop portfolios was smaller compared to potato and pepper itsstandard deviation decreased The difference between the three- and the five-crop portfoliosin mean and standard deviation was only minor

16

Table 4 Risks adjusted revenue for the analysed period from 1996 to 2011

Crop selection Mean (million KRW) SD Sharpe ratio

Single croprice 1085 173 627

beans 596 175 340potato 3092 770 401radish 1476 298 495

cabbage 2288 435 526pepper 3294 1420 232

three-crop portfolio 2023 532 380five-crop portfolio 2412 560 430

4 Discussion

An advantage of decomposing the time series is that we can not only identify the mostfluctuating crop over time but also quantify different components of fluctuations in eachcrop Fluctuations on larger time scales (trend and seasonality) are easier for farmers toface than short-time variations which are more difficult to address in the planning processIn order to distinguish four time scales of fluctuations in each crop selection we calculatedthe ratio of eigenvalue for each time scale The ratio of eigenvalue stands for the quality ofthe reconstruction of the original time series by a certain component The larger this ratiothe more important the component will be for the reconstruction Among four time scalesthe first and the second scales can be interpreted as trend and seasonality respectively thethird and the fourth scales however were too short to be identified

Farmersrsquo decision on which crop to grow how to allocate the land to grow multiple cropsand when to harvest and sell them plays a crucial role to secure their revenue (Fafchamps1992 Kantanantha et al 2010 Klasen et al 2013) Our result showed that each crop had adifferent fluctuation pattern that highly influenced the farm revenue depending on farmersrsquocrop selection The sum of the first two ratios of eigenvalues for crop price ranged from 548(pepper) to 884 (rice) The larger the contribution of trend and seasonality the less short-time variability is contained in the data Four of the six analysed crops contained notableseasonal patterns The SSA of the three- and the five-crop portfolios also revealed thatimportant seasonal variation still remained in the monthly price data Therefore seasonalityprobably has an important impact on farmersrsquo decisions regarding the times for harvestingor marketing of their crops

The risk adjusted revenue calculated with the Sharpe ratio allows us to compare how muchrevenue standardised per 1 of revenue can be guaranteed for farmers in each crop selectionThe combination of these methods provides more information to support farmersrsquo decision oncrop selection Although the results of SSA and the Sharpe ratio showed that rice and beanfarming were the most stable they provided the lowest revenue The revenue of the three-and the five-crop portfolios was more than two times larger than in rice farming howeverat the same time the standard deviation tripled (Table 4) It indicates that the diversified

17

Time

Pric

e (U

SDto

n)

500

1000

1500

2000

1996 1998 2000 2002 2004 2006 2008 2010 2012

Korean domestic rice price World rice price

200

600

1000 original data gt 24 months (684)

Time

minus10

050

6minus24 months (154)

Time

minus10

00

100

3minus59 months (107)

Time

minus40

040

lt 29 months (54)

1991 1997 2003 2009 2015

Pric

e (U

SD

ton)

Year

Figure 7 Korean domestic rice price converted in USDton and world rice price in USDton (left) SSAdecomposition of the world rice price (right) Four groups of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it The world rice data was Thailand nominal price quote obtained from the World BankGlobal Economic Monitor (GEM) Commodities The exchange rate from Korean Won to USD for each yearwas obtained from the World Bank World Development Indicators

farming could support larger revenue This is in accordance with the study by Bhattacharyya(2008) who showed that a rice dominated farming system in India was changed to high-valuecrops for larger revenue Furthermore an analysis in Argentina showed that diversifiedfarming increased the mean return on capital with a lower coefficient of variation (Pacın andOesterheld 2014) Hence the multiple crop farming may be a means of enhancing revenue(Ali et al 2004 Winters et al 2006 Pacın and Oesterheld 2014 Rahman and Kazal 2015)However the diversification took place slowly due to agricultural subsidies concentrated ona certain crop such as rice in India (Bhattacharyya 2008) This might also be the case inSouth Korea

To examine the artificial stability of the rice price in South Korea we compared thedomestic rice price with the world rice price in USD (Figure 7) As the exchange rate variesbetween years the domestic rice price converted in USD fluctuated more compared to theone in KRW We refer to the SSA result of the rice price in KRW to keep consistency unlessmentioned While the world rice price increased drastically in 2008 as a result of the oilcrisis (Figure 7 right) the Korean domestic price was not affected by it and remained stable(Figure 3 (a)) Overall rice price in the global market fluctuates more than in the SouthKorean domestic market (Baffes and Cosic 2013) Furthermore the Korean domestic priceis more than double or triple the world price ndash the result of a substantial governmentalsupport (Figure 7 left)

South Korea used to have a higher protection for domestic rice farming mainly throughtariff and non-tariff barriers in comparison to other OECD countries (Aksoy 2005) Amongother conventional crops Korean subsidy policy focuses particularly on rice farming by sup-

18

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

1600

1800

2000

original data gt 24 months (701)(a)

Time

minus50

50

6minus24 months (183)

Time

minus20

20

3minus59 months (89)

Time

minus10

515lt 29 months (26)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

5000

8000

original data gt 24 months (546)(b)

Time

minus20

0020

006minus24 months (303)

Time

minus20

040

0

3minus59 months (111)

Time

minus20

00

200

lt 29 months (4)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

050

015

0025

00

original data gt 24 months (314)(c)

Time

minus40

040

06minus24 months (357)

Time

minus30

030

0 3minus59 months (237)

Time

minus10

020

0lt 29 months (92)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500 original data gt 24 months (238)(d)

Time

minus20

040

06minus24 months (436)

Time

minus20

020

0 3minus59 months (232)

Time

minus10

010

0lt 29 months (95)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

500

1000

1500

original data gt 24 months (252)(e)

Time

minus50

050

0

6minus24 months (39)

Time

minus20

020

0 3minus59 months (234)

Time

minus20

020

0

lt 29 months (124)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

2000

6000

1200

0 original data gt 24 months (122)(f)

Time

minus40

0040

006minus24 months (426)

Time

minus20

0020

00 3minus59 months (277)

Time

minus20

0020

00lt 29 months (175)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 3 SSA decomposition of the crop prices (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper Four groups of fluctuation were considered larger than 24 months (trend) 6ndash24 months (sea-sonality) 3ndash59 months smaller than 29 months The number in parenthesis shows the ratio of eigenvaluesThe trend component contains the mean the others show the variability around it

13

1000

3000

5000

original data gt 24 months (239)(a)

Time

minus20

0020

006minus24 months (352)

Time

minus50

050

0 3minus59 months (259)

Timeminus

400

400lt 29 months (15)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

1000

3000

5000

original data gt 24 months (204)(b)

Time

minus20

0020

006minus24 months (408)

Time

minus50

050

0 3minus59 months (236)

Time

minus40

040

0lt 29 months (152)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 4 SSA decomposition of the portfolio prices (a) three-crops portfolio (beans (350) pepper (325)and cabbage (325)) and (b) five-crops portfolio (potato (29) pepper (277) beans (174) cabbage(144) and radish (115))For both portfolio four periods of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it

the contribution of the trend decreased from 546 to 204 Additionally the contributionof the seasonal fluctuation remained comparable to the other crops that have a strong sea-sonal pattern In summary the results of SSA decomposition were similar to the portfoliocomposed of three crops Indeed the summed contributions of the larger time scales (trendand seasonality) as well as those on the smaller time scales differed only slightly

33 Crop yield fluctuations

An in-depth analysis of seasonality was not possible because the time series of yieldconsisted of annual measurements Therefore we only extracted the trend and calculatedthe dominant frequency of the remaining periodicities (Figure 5) The result of SSA showedthat the contribution of the trend varied from 333 to 665 Accordingly the importanceof periodicities ranged from 335 to 667 Their dominant frequency covered 25 years to107 years

In general crop yield had an upwards trend during the analysed period except forradish and cabbage (Figure 5) Four of the six analysed crops namely rice beans potatoand pepper showed increasing trends in the yields In contrast the yield of radish andcabbage had decreased during the 23-year analysed period There were more negative thanpositive extreme values outside the range of the standard deviation of the trend Additionallythe amplitude of negative values was often larger than that of positive values (Figure 5)Interestingly large negative values occurred in different years for different crops In 1980and 1993 for example the rice yield decreased sharply whereas there was a relatively high

14

23

45

6

original data trend (457)(a)

Time

minus2

01

2

25 years (543)

1965 1975 1985 1995 2005

Yie

ld (

ton

ha)

Year

10

12

14

16

18

20

original data trend (333)(b)

Time

minus0

30

00

3

4 years (667)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

1015

2025

3035

40 original data trend (424)(c)

Time

minus10

0527 years (576)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3034

3842 original data trend (349)

(d)

Time

minus6

04

8

46 years (651)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3540

4550

5560 original data trend (344)

(e)

Time

minus10

0523 years (656)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

24

68

1012 original data trend (665)

(f)

Time

minus3

minus1

13

107 years (335)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

Figure 5 SSA decomposition of the crop yield (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper The number in parenthesis shows the ratio of eigenvalues The trend component contains themean the others show the variability around it The yellow area shows plusmn standard deviation around thetrend component Note that the time scale is years and not months as for the price data Fluctuations withperiods of 23 years and 16 years (trend) were chosen for rice and the other crops respectively

15

Year

Rea

l Rev

enue

(M

illio

n K

RW

haminus1

year

minus1)

020

4060

1996 1998 2000 2002 2004 2006 2008 2010

ricebeans

potatoradisch

cabbagepepper

threeminuscrop portfoliofiveminuscrop portfolio

Figure 6 Real revenue for single crops and the empirical crop portfolios

yield in potato in the same year In 1996 the radish yield was very low and the rice yieldmoderately high (See Figure 5 and Supplementary Figure SF4)

The sharp drops of yield often followed damages caused by unusual weather eventsEspecially in 1980 the rice yield reached only 587 of the target yield of South Koreadue to low temperature (Park et al 2010) In 1987 and 2010 radish and cabbage werealso influenced by bad weather (Kwon 2012) Frequent rain and lack of sunlight duringseeding period harmed stabilising seeds (Han and Kim 2010) In addition the yield ofradish and cabbage has declined as the consumption decreases and imports increase (KoreaRural Economic Institute 2015) Actually the import of cabbage has increased since 2003and westernised eating habits of South Koreans has decreased its consumption by 2 peryear since 2002 (Korea Rural Economic Institute 2015)

34 Risk adjusted revenue

The revenue and the Sharpe ratio for each crop portfolio are depicted in Figure 6 andTable 4 The Sharpe ratio is often used to assess the portfolio performance (Blank 1990Roche and McQuinn 2004 Gaydon et al 2012) For example Roche and McQuinn (2004)calculated the Sharpe ratio for the farm land allocation portfolio for grains and Gaydon et al(2012) used it for comparing water management options and their contribution to the farmincome

Figure 6 shows the temporal change of the real revenue of single crops and three-and five-crop portfolios Large differences between the six main crops were observed Rice and beansshowed a stable but the smallest and decreasing revenue compared to the other crops overthe analysed period Pepper showed the highest revenue with the highest standard deviation(Table 4) In the portfolio the mean revenue doubled or tripled and the standard deviationincreased with the number of crops compared to rice and bean single crop farming Althoughthe mean revenue of the crop portfolios was smaller compared to potato and pepper itsstandard deviation decreased The difference between the three- and the five-crop portfoliosin mean and standard deviation was only minor

16

Table 4 Risks adjusted revenue for the analysed period from 1996 to 2011

Crop selection Mean (million KRW) SD Sharpe ratio

Single croprice 1085 173 627

beans 596 175 340potato 3092 770 401radish 1476 298 495

cabbage 2288 435 526pepper 3294 1420 232

three-crop portfolio 2023 532 380five-crop portfolio 2412 560 430

4 Discussion

An advantage of decomposing the time series is that we can not only identify the mostfluctuating crop over time but also quantify different components of fluctuations in eachcrop Fluctuations on larger time scales (trend and seasonality) are easier for farmers toface than short-time variations which are more difficult to address in the planning processIn order to distinguish four time scales of fluctuations in each crop selection we calculatedthe ratio of eigenvalue for each time scale The ratio of eigenvalue stands for the quality ofthe reconstruction of the original time series by a certain component The larger this ratiothe more important the component will be for the reconstruction Among four time scalesthe first and the second scales can be interpreted as trend and seasonality respectively thethird and the fourth scales however were too short to be identified

Farmersrsquo decision on which crop to grow how to allocate the land to grow multiple cropsand when to harvest and sell them plays a crucial role to secure their revenue (Fafchamps1992 Kantanantha et al 2010 Klasen et al 2013) Our result showed that each crop had adifferent fluctuation pattern that highly influenced the farm revenue depending on farmersrsquocrop selection The sum of the first two ratios of eigenvalues for crop price ranged from 548(pepper) to 884 (rice) The larger the contribution of trend and seasonality the less short-time variability is contained in the data Four of the six analysed crops contained notableseasonal patterns The SSA of the three- and the five-crop portfolios also revealed thatimportant seasonal variation still remained in the monthly price data Therefore seasonalityprobably has an important impact on farmersrsquo decisions regarding the times for harvestingor marketing of their crops

The risk adjusted revenue calculated with the Sharpe ratio allows us to compare how muchrevenue standardised per 1 of revenue can be guaranteed for farmers in each crop selectionThe combination of these methods provides more information to support farmersrsquo decision oncrop selection Although the results of SSA and the Sharpe ratio showed that rice and beanfarming were the most stable they provided the lowest revenue The revenue of the three-and the five-crop portfolios was more than two times larger than in rice farming howeverat the same time the standard deviation tripled (Table 4) It indicates that the diversified

17

Time

Pric

e (U

SDto

n)

500

1000

1500

2000

1996 1998 2000 2002 2004 2006 2008 2010 2012

Korean domestic rice price World rice price

200

600

1000 original data gt 24 months (684)

Time

minus10

050

6minus24 months (154)

Time

minus10

00

100

3minus59 months (107)

Time

minus40

040

lt 29 months (54)

1991 1997 2003 2009 2015

Pric

e (U

SD

ton)

Year

Figure 7 Korean domestic rice price converted in USDton and world rice price in USDton (left) SSAdecomposition of the world rice price (right) Four groups of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it The world rice data was Thailand nominal price quote obtained from the World BankGlobal Economic Monitor (GEM) Commodities The exchange rate from Korean Won to USD for each yearwas obtained from the World Bank World Development Indicators

farming could support larger revenue This is in accordance with the study by Bhattacharyya(2008) who showed that a rice dominated farming system in India was changed to high-valuecrops for larger revenue Furthermore an analysis in Argentina showed that diversifiedfarming increased the mean return on capital with a lower coefficient of variation (Pacın andOesterheld 2014) Hence the multiple crop farming may be a means of enhancing revenue(Ali et al 2004 Winters et al 2006 Pacın and Oesterheld 2014 Rahman and Kazal 2015)However the diversification took place slowly due to agricultural subsidies concentrated ona certain crop such as rice in India (Bhattacharyya 2008) This might also be the case inSouth Korea

To examine the artificial stability of the rice price in South Korea we compared thedomestic rice price with the world rice price in USD (Figure 7) As the exchange rate variesbetween years the domestic rice price converted in USD fluctuated more compared to theone in KRW We refer to the SSA result of the rice price in KRW to keep consistency unlessmentioned While the world rice price increased drastically in 2008 as a result of the oilcrisis (Figure 7 right) the Korean domestic price was not affected by it and remained stable(Figure 3 (a)) Overall rice price in the global market fluctuates more than in the SouthKorean domestic market (Baffes and Cosic 2013) Furthermore the Korean domestic priceis more than double or triple the world price ndash the result of a substantial governmentalsupport (Figure 7 left)

South Korea used to have a higher protection for domestic rice farming mainly throughtariff and non-tariff barriers in comparison to other OECD countries (Aksoy 2005) Amongother conventional crops Korean subsidy policy focuses particularly on rice farming by sup-

18

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

1000

3000

5000

original data gt 24 months (239)(a)

Time

minus20

0020

006minus24 months (352)

Time

minus50

050

0 3minus59 months (259)

Timeminus

400

400lt 29 months (15)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

1000

3000

5000

original data gt 24 months (204)(b)

Time

minus20

0020

006minus24 months (408)

Time

minus50

050

0 3minus59 months (236)

Time

minus40

040

0lt 29 months (152)

1996 1998 2000 2002 2004 2006 2008 2010 2012

Pric

e (K

RW

kg)

Year

Figure 4 SSA decomposition of the portfolio prices (a) three-crops portfolio (beans (350) pepper (325)and cabbage (325)) and (b) five-crops portfolio (potato (29) pepper (277) beans (174) cabbage(144) and radish (115))For both portfolio four periods of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it

the contribution of the trend decreased from 546 to 204 Additionally the contributionof the seasonal fluctuation remained comparable to the other crops that have a strong sea-sonal pattern In summary the results of SSA decomposition were similar to the portfoliocomposed of three crops Indeed the summed contributions of the larger time scales (trendand seasonality) as well as those on the smaller time scales differed only slightly

33 Crop yield fluctuations

An in-depth analysis of seasonality was not possible because the time series of yieldconsisted of annual measurements Therefore we only extracted the trend and calculatedthe dominant frequency of the remaining periodicities (Figure 5) The result of SSA showedthat the contribution of the trend varied from 333 to 665 Accordingly the importanceof periodicities ranged from 335 to 667 Their dominant frequency covered 25 years to107 years

In general crop yield had an upwards trend during the analysed period except forradish and cabbage (Figure 5) Four of the six analysed crops namely rice beans potatoand pepper showed increasing trends in the yields In contrast the yield of radish andcabbage had decreased during the 23-year analysed period There were more negative thanpositive extreme values outside the range of the standard deviation of the trend Additionallythe amplitude of negative values was often larger than that of positive values (Figure 5)Interestingly large negative values occurred in different years for different crops In 1980and 1993 for example the rice yield decreased sharply whereas there was a relatively high

14

23

45

6

original data trend (457)(a)

Time

minus2

01

2

25 years (543)

1965 1975 1985 1995 2005

Yie

ld (

ton

ha)

Year

10

12

14

16

18

20

original data trend (333)(b)

Time

minus0

30

00

3

4 years (667)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

1015

2025

3035

40 original data trend (424)(c)

Time

minus10

0527 years (576)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3034

3842 original data trend (349)

(d)

Time

minus6

04

8

46 years (651)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3540

4550

5560 original data trend (344)

(e)

Time

minus10

0523 years (656)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

24

68

1012 original data trend (665)

(f)

Time

minus3

minus1

13

107 years (335)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

Figure 5 SSA decomposition of the crop yield (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper The number in parenthesis shows the ratio of eigenvalues The trend component contains themean the others show the variability around it The yellow area shows plusmn standard deviation around thetrend component Note that the time scale is years and not months as for the price data Fluctuations withperiods of 23 years and 16 years (trend) were chosen for rice and the other crops respectively

15

Year

Rea

l Rev

enue

(M

illio

n K

RW

haminus1

year

minus1)

020

4060

1996 1998 2000 2002 2004 2006 2008 2010

ricebeans

potatoradisch

cabbagepepper

threeminuscrop portfoliofiveminuscrop portfolio

Figure 6 Real revenue for single crops and the empirical crop portfolios

yield in potato in the same year In 1996 the radish yield was very low and the rice yieldmoderately high (See Figure 5 and Supplementary Figure SF4)

The sharp drops of yield often followed damages caused by unusual weather eventsEspecially in 1980 the rice yield reached only 587 of the target yield of South Koreadue to low temperature (Park et al 2010) In 1987 and 2010 radish and cabbage werealso influenced by bad weather (Kwon 2012) Frequent rain and lack of sunlight duringseeding period harmed stabilising seeds (Han and Kim 2010) In addition the yield ofradish and cabbage has declined as the consumption decreases and imports increase (KoreaRural Economic Institute 2015) Actually the import of cabbage has increased since 2003and westernised eating habits of South Koreans has decreased its consumption by 2 peryear since 2002 (Korea Rural Economic Institute 2015)

34 Risk adjusted revenue

The revenue and the Sharpe ratio for each crop portfolio are depicted in Figure 6 andTable 4 The Sharpe ratio is often used to assess the portfolio performance (Blank 1990Roche and McQuinn 2004 Gaydon et al 2012) For example Roche and McQuinn (2004)calculated the Sharpe ratio for the farm land allocation portfolio for grains and Gaydon et al(2012) used it for comparing water management options and their contribution to the farmincome

Figure 6 shows the temporal change of the real revenue of single crops and three-and five-crop portfolios Large differences between the six main crops were observed Rice and beansshowed a stable but the smallest and decreasing revenue compared to the other crops overthe analysed period Pepper showed the highest revenue with the highest standard deviation(Table 4) In the portfolio the mean revenue doubled or tripled and the standard deviationincreased with the number of crops compared to rice and bean single crop farming Althoughthe mean revenue of the crop portfolios was smaller compared to potato and pepper itsstandard deviation decreased The difference between the three- and the five-crop portfoliosin mean and standard deviation was only minor

16

Table 4 Risks adjusted revenue for the analysed period from 1996 to 2011

Crop selection Mean (million KRW) SD Sharpe ratio

Single croprice 1085 173 627

beans 596 175 340potato 3092 770 401radish 1476 298 495

cabbage 2288 435 526pepper 3294 1420 232

three-crop portfolio 2023 532 380five-crop portfolio 2412 560 430

4 Discussion

An advantage of decomposing the time series is that we can not only identify the mostfluctuating crop over time but also quantify different components of fluctuations in eachcrop Fluctuations on larger time scales (trend and seasonality) are easier for farmers toface than short-time variations which are more difficult to address in the planning processIn order to distinguish four time scales of fluctuations in each crop selection we calculatedthe ratio of eigenvalue for each time scale The ratio of eigenvalue stands for the quality ofthe reconstruction of the original time series by a certain component The larger this ratiothe more important the component will be for the reconstruction Among four time scalesthe first and the second scales can be interpreted as trend and seasonality respectively thethird and the fourth scales however were too short to be identified

Farmersrsquo decision on which crop to grow how to allocate the land to grow multiple cropsand when to harvest and sell them plays a crucial role to secure their revenue (Fafchamps1992 Kantanantha et al 2010 Klasen et al 2013) Our result showed that each crop had adifferent fluctuation pattern that highly influenced the farm revenue depending on farmersrsquocrop selection The sum of the first two ratios of eigenvalues for crop price ranged from 548(pepper) to 884 (rice) The larger the contribution of trend and seasonality the less short-time variability is contained in the data Four of the six analysed crops contained notableseasonal patterns The SSA of the three- and the five-crop portfolios also revealed thatimportant seasonal variation still remained in the monthly price data Therefore seasonalityprobably has an important impact on farmersrsquo decisions regarding the times for harvestingor marketing of their crops

The risk adjusted revenue calculated with the Sharpe ratio allows us to compare how muchrevenue standardised per 1 of revenue can be guaranteed for farmers in each crop selectionThe combination of these methods provides more information to support farmersrsquo decision oncrop selection Although the results of SSA and the Sharpe ratio showed that rice and beanfarming were the most stable they provided the lowest revenue The revenue of the three-and the five-crop portfolios was more than two times larger than in rice farming howeverat the same time the standard deviation tripled (Table 4) It indicates that the diversified

17

Time

Pric

e (U

SDto

n)

500

1000

1500

2000

1996 1998 2000 2002 2004 2006 2008 2010 2012

Korean domestic rice price World rice price

200

600

1000 original data gt 24 months (684)

Time

minus10

050

6minus24 months (154)

Time

minus10

00

100

3minus59 months (107)

Time

minus40

040

lt 29 months (54)

1991 1997 2003 2009 2015

Pric

e (U

SD

ton)

Year

Figure 7 Korean domestic rice price converted in USDton and world rice price in USDton (left) SSAdecomposition of the world rice price (right) Four groups of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it The world rice data was Thailand nominal price quote obtained from the World BankGlobal Economic Monitor (GEM) Commodities The exchange rate from Korean Won to USD for each yearwas obtained from the World Bank World Development Indicators

farming could support larger revenue This is in accordance with the study by Bhattacharyya(2008) who showed that a rice dominated farming system in India was changed to high-valuecrops for larger revenue Furthermore an analysis in Argentina showed that diversifiedfarming increased the mean return on capital with a lower coefficient of variation (Pacın andOesterheld 2014) Hence the multiple crop farming may be a means of enhancing revenue(Ali et al 2004 Winters et al 2006 Pacın and Oesterheld 2014 Rahman and Kazal 2015)However the diversification took place slowly due to agricultural subsidies concentrated ona certain crop such as rice in India (Bhattacharyya 2008) This might also be the case inSouth Korea

To examine the artificial stability of the rice price in South Korea we compared thedomestic rice price with the world rice price in USD (Figure 7) As the exchange rate variesbetween years the domestic rice price converted in USD fluctuated more compared to theone in KRW We refer to the SSA result of the rice price in KRW to keep consistency unlessmentioned While the world rice price increased drastically in 2008 as a result of the oilcrisis (Figure 7 right) the Korean domestic price was not affected by it and remained stable(Figure 3 (a)) Overall rice price in the global market fluctuates more than in the SouthKorean domestic market (Baffes and Cosic 2013) Furthermore the Korean domestic priceis more than double or triple the world price ndash the result of a substantial governmentalsupport (Figure 7 left)

South Korea used to have a higher protection for domestic rice farming mainly throughtariff and non-tariff barriers in comparison to other OECD countries (Aksoy 2005) Amongother conventional crops Korean subsidy policy focuses particularly on rice farming by sup-

18

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

23

45

6

original data trend (457)(a)

Time

minus2

01

2

25 years (543)

1965 1975 1985 1995 2005

Yie

ld (

ton

ha)

Year

10

12

14

16

18

20

original data trend (333)(b)

Time

minus0

30

00

3

4 years (667)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

1015

2025

3035

40 original data trend (424)(c)

Time

minus10

0527 years (576)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3034

3842 original data trend (349)

(d)

Time

minus6

04

8

46 years (651)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

3540

4550

5560 original data trend (344)

(e)

Time

minus10

0523 years (656)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

24

68

1012 original data trend (665)

(f)

Time

minus3

minus1

13

107 years (335)

1980 1985 1990 1995 2000 2005 2010

Yie

ld (

ton

ha)

Year

Figure 5 SSA decomposition of the crop yield (a) rice (b) beans (c) potato (d) radish (e) cabbage and(f) pepper The number in parenthesis shows the ratio of eigenvalues The trend component contains themean the others show the variability around it The yellow area shows plusmn standard deviation around thetrend component Note that the time scale is years and not months as for the price data Fluctuations withperiods of 23 years and 16 years (trend) were chosen for rice and the other crops respectively

15

Year

Rea

l Rev

enue

(M

illio

n K

RW

haminus1

year

minus1)

020

4060

1996 1998 2000 2002 2004 2006 2008 2010

ricebeans

potatoradisch

cabbagepepper

threeminuscrop portfoliofiveminuscrop portfolio

Figure 6 Real revenue for single crops and the empirical crop portfolios

yield in potato in the same year In 1996 the radish yield was very low and the rice yieldmoderately high (See Figure 5 and Supplementary Figure SF4)

The sharp drops of yield often followed damages caused by unusual weather eventsEspecially in 1980 the rice yield reached only 587 of the target yield of South Koreadue to low temperature (Park et al 2010) In 1987 and 2010 radish and cabbage werealso influenced by bad weather (Kwon 2012) Frequent rain and lack of sunlight duringseeding period harmed stabilising seeds (Han and Kim 2010) In addition the yield ofradish and cabbage has declined as the consumption decreases and imports increase (KoreaRural Economic Institute 2015) Actually the import of cabbage has increased since 2003and westernised eating habits of South Koreans has decreased its consumption by 2 peryear since 2002 (Korea Rural Economic Institute 2015)

34 Risk adjusted revenue

The revenue and the Sharpe ratio for each crop portfolio are depicted in Figure 6 andTable 4 The Sharpe ratio is often used to assess the portfolio performance (Blank 1990Roche and McQuinn 2004 Gaydon et al 2012) For example Roche and McQuinn (2004)calculated the Sharpe ratio for the farm land allocation portfolio for grains and Gaydon et al(2012) used it for comparing water management options and their contribution to the farmincome

Figure 6 shows the temporal change of the real revenue of single crops and three-and five-crop portfolios Large differences between the six main crops were observed Rice and beansshowed a stable but the smallest and decreasing revenue compared to the other crops overthe analysed period Pepper showed the highest revenue with the highest standard deviation(Table 4) In the portfolio the mean revenue doubled or tripled and the standard deviationincreased with the number of crops compared to rice and bean single crop farming Althoughthe mean revenue of the crop portfolios was smaller compared to potato and pepper itsstandard deviation decreased The difference between the three- and the five-crop portfoliosin mean and standard deviation was only minor

16

Table 4 Risks adjusted revenue for the analysed period from 1996 to 2011

Crop selection Mean (million KRW) SD Sharpe ratio

Single croprice 1085 173 627

beans 596 175 340potato 3092 770 401radish 1476 298 495

cabbage 2288 435 526pepper 3294 1420 232

three-crop portfolio 2023 532 380five-crop portfolio 2412 560 430

4 Discussion

An advantage of decomposing the time series is that we can not only identify the mostfluctuating crop over time but also quantify different components of fluctuations in eachcrop Fluctuations on larger time scales (trend and seasonality) are easier for farmers toface than short-time variations which are more difficult to address in the planning processIn order to distinguish four time scales of fluctuations in each crop selection we calculatedthe ratio of eigenvalue for each time scale The ratio of eigenvalue stands for the quality ofthe reconstruction of the original time series by a certain component The larger this ratiothe more important the component will be for the reconstruction Among four time scalesthe first and the second scales can be interpreted as trend and seasonality respectively thethird and the fourth scales however were too short to be identified

Farmersrsquo decision on which crop to grow how to allocate the land to grow multiple cropsand when to harvest and sell them plays a crucial role to secure their revenue (Fafchamps1992 Kantanantha et al 2010 Klasen et al 2013) Our result showed that each crop had adifferent fluctuation pattern that highly influenced the farm revenue depending on farmersrsquocrop selection The sum of the first two ratios of eigenvalues for crop price ranged from 548(pepper) to 884 (rice) The larger the contribution of trend and seasonality the less short-time variability is contained in the data Four of the six analysed crops contained notableseasonal patterns The SSA of the three- and the five-crop portfolios also revealed thatimportant seasonal variation still remained in the monthly price data Therefore seasonalityprobably has an important impact on farmersrsquo decisions regarding the times for harvestingor marketing of their crops

The risk adjusted revenue calculated with the Sharpe ratio allows us to compare how muchrevenue standardised per 1 of revenue can be guaranteed for farmers in each crop selectionThe combination of these methods provides more information to support farmersrsquo decision oncrop selection Although the results of SSA and the Sharpe ratio showed that rice and beanfarming were the most stable they provided the lowest revenue The revenue of the three-and the five-crop portfolios was more than two times larger than in rice farming howeverat the same time the standard deviation tripled (Table 4) It indicates that the diversified

17

Time

Pric

e (U

SDto

n)

500

1000

1500

2000

1996 1998 2000 2002 2004 2006 2008 2010 2012

Korean domestic rice price World rice price

200

600

1000 original data gt 24 months (684)

Time

minus10

050

6minus24 months (154)

Time

minus10

00

100

3minus59 months (107)

Time

minus40

040

lt 29 months (54)

1991 1997 2003 2009 2015

Pric

e (U

SD

ton)

Year

Figure 7 Korean domestic rice price converted in USDton and world rice price in USDton (left) SSAdecomposition of the world rice price (right) Four groups of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it The world rice data was Thailand nominal price quote obtained from the World BankGlobal Economic Monitor (GEM) Commodities The exchange rate from Korean Won to USD for each yearwas obtained from the World Bank World Development Indicators

farming could support larger revenue This is in accordance with the study by Bhattacharyya(2008) who showed that a rice dominated farming system in India was changed to high-valuecrops for larger revenue Furthermore an analysis in Argentina showed that diversifiedfarming increased the mean return on capital with a lower coefficient of variation (Pacın andOesterheld 2014) Hence the multiple crop farming may be a means of enhancing revenue(Ali et al 2004 Winters et al 2006 Pacın and Oesterheld 2014 Rahman and Kazal 2015)However the diversification took place slowly due to agricultural subsidies concentrated ona certain crop such as rice in India (Bhattacharyya 2008) This might also be the case inSouth Korea

To examine the artificial stability of the rice price in South Korea we compared thedomestic rice price with the world rice price in USD (Figure 7) As the exchange rate variesbetween years the domestic rice price converted in USD fluctuated more compared to theone in KRW We refer to the SSA result of the rice price in KRW to keep consistency unlessmentioned While the world rice price increased drastically in 2008 as a result of the oilcrisis (Figure 7 right) the Korean domestic price was not affected by it and remained stable(Figure 3 (a)) Overall rice price in the global market fluctuates more than in the SouthKorean domestic market (Baffes and Cosic 2013) Furthermore the Korean domestic priceis more than double or triple the world price ndash the result of a substantial governmentalsupport (Figure 7 left)

South Korea used to have a higher protection for domestic rice farming mainly throughtariff and non-tariff barriers in comparison to other OECD countries (Aksoy 2005) Amongother conventional crops Korean subsidy policy focuses particularly on rice farming by sup-

18

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

Year

Rea

l Rev

enue

(M

illio

n K

RW

haminus1

year

minus1)

020

4060

1996 1998 2000 2002 2004 2006 2008 2010

ricebeans

potatoradisch

cabbagepepper

threeminuscrop portfoliofiveminuscrop portfolio

Figure 6 Real revenue for single crops and the empirical crop portfolios

yield in potato in the same year In 1996 the radish yield was very low and the rice yieldmoderately high (See Figure 5 and Supplementary Figure SF4)

The sharp drops of yield often followed damages caused by unusual weather eventsEspecially in 1980 the rice yield reached only 587 of the target yield of South Koreadue to low temperature (Park et al 2010) In 1987 and 2010 radish and cabbage werealso influenced by bad weather (Kwon 2012) Frequent rain and lack of sunlight duringseeding period harmed stabilising seeds (Han and Kim 2010) In addition the yield ofradish and cabbage has declined as the consumption decreases and imports increase (KoreaRural Economic Institute 2015) Actually the import of cabbage has increased since 2003and westernised eating habits of South Koreans has decreased its consumption by 2 peryear since 2002 (Korea Rural Economic Institute 2015)

34 Risk adjusted revenue

The revenue and the Sharpe ratio for each crop portfolio are depicted in Figure 6 andTable 4 The Sharpe ratio is often used to assess the portfolio performance (Blank 1990Roche and McQuinn 2004 Gaydon et al 2012) For example Roche and McQuinn (2004)calculated the Sharpe ratio for the farm land allocation portfolio for grains and Gaydon et al(2012) used it for comparing water management options and their contribution to the farmincome

Figure 6 shows the temporal change of the real revenue of single crops and three-and five-crop portfolios Large differences between the six main crops were observed Rice and beansshowed a stable but the smallest and decreasing revenue compared to the other crops overthe analysed period Pepper showed the highest revenue with the highest standard deviation(Table 4) In the portfolio the mean revenue doubled or tripled and the standard deviationincreased with the number of crops compared to rice and bean single crop farming Althoughthe mean revenue of the crop portfolios was smaller compared to potato and pepper itsstandard deviation decreased The difference between the three- and the five-crop portfoliosin mean and standard deviation was only minor

16

Table 4 Risks adjusted revenue for the analysed period from 1996 to 2011

Crop selection Mean (million KRW) SD Sharpe ratio

Single croprice 1085 173 627

beans 596 175 340potato 3092 770 401radish 1476 298 495

cabbage 2288 435 526pepper 3294 1420 232

three-crop portfolio 2023 532 380five-crop portfolio 2412 560 430

4 Discussion

An advantage of decomposing the time series is that we can not only identify the mostfluctuating crop over time but also quantify different components of fluctuations in eachcrop Fluctuations on larger time scales (trend and seasonality) are easier for farmers toface than short-time variations which are more difficult to address in the planning processIn order to distinguish four time scales of fluctuations in each crop selection we calculatedthe ratio of eigenvalue for each time scale The ratio of eigenvalue stands for the quality ofthe reconstruction of the original time series by a certain component The larger this ratiothe more important the component will be for the reconstruction Among four time scalesthe first and the second scales can be interpreted as trend and seasonality respectively thethird and the fourth scales however were too short to be identified

Farmersrsquo decision on which crop to grow how to allocate the land to grow multiple cropsand when to harvest and sell them plays a crucial role to secure their revenue (Fafchamps1992 Kantanantha et al 2010 Klasen et al 2013) Our result showed that each crop had adifferent fluctuation pattern that highly influenced the farm revenue depending on farmersrsquocrop selection The sum of the first two ratios of eigenvalues for crop price ranged from 548(pepper) to 884 (rice) The larger the contribution of trend and seasonality the less short-time variability is contained in the data Four of the six analysed crops contained notableseasonal patterns The SSA of the three- and the five-crop portfolios also revealed thatimportant seasonal variation still remained in the monthly price data Therefore seasonalityprobably has an important impact on farmersrsquo decisions regarding the times for harvestingor marketing of their crops

The risk adjusted revenue calculated with the Sharpe ratio allows us to compare how muchrevenue standardised per 1 of revenue can be guaranteed for farmers in each crop selectionThe combination of these methods provides more information to support farmersrsquo decision oncrop selection Although the results of SSA and the Sharpe ratio showed that rice and beanfarming were the most stable they provided the lowest revenue The revenue of the three-and the five-crop portfolios was more than two times larger than in rice farming howeverat the same time the standard deviation tripled (Table 4) It indicates that the diversified

17

Time

Pric

e (U

SDto

n)

500

1000

1500

2000

1996 1998 2000 2002 2004 2006 2008 2010 2012

Korean domestic rice price World rice price

200

600

1000 original data gt 24 months (684)

Time

minus10

050

6minus24 months (154)

Time

minus10

00

100

3minus59 months (107)

Time

minus40

040

lt 29 months (54)

1991 1997 2003 2009 2015

Pric

e (U

SD

ton)

Year

Figure 7 Korean domestic rice price converted in USDton and world rice price in USDton (left) SSAdecomposition of the world rice price (right) Four groups of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it The world rice data was Thailand nominal price quote obtained from the World BankGlobal Economic Monitor (GEM) Commodities The exchange rate from Korean Won to USD for each yearwas obtained from the World Bank World Development Indicators

farming could support larger revenue This is in accordance with the study by Bhattacharyya(2008) who showed that a rice dominated farming system in India was changed to high-valuecrops for larger revenue Furthermore an analysis in Argentina showed that diversifiedfarming increased the mean return on capital with a lower coefficient of variation (Pacın andOesterheld 2014) Hence the multiple crop farming may be a means of enhancing revenue(Ali et al 2004 Winters et al 2006 Pacın and Oesterheld 2014 Rahman and Kazal 2015)However the diversification took place slowly due to agricultural subsidies concentrated ona certain crop such as rice in India (Bhattacharyya 2008) This might also be the case inSouth Korea

To examine the artificial stability of the rice price in South Korea we compared thedomestic rice price with the world rice price in USD (Figure 7) As the exchange rate variesbetween years the domestic rice price converted in USD fluctuated more compared to theone in KRW We refer to the SSA result of the rice price in KRW to keep consistency unlessmentioned While the world rice price increased drastically in 2008 as a result of the oilcrisis (Figure 7 right) the Korean domestic price was not affected by it and remained stable(Figure 3 (a)) Overall rice price in the global market fluctuates more than in the SouthKorean domestic market (Baffes and Cosic 2013) Furthermore the Korean domestic priceis more than double or triple the world price ndash the result of a substantial governmentalsupport (Figure 7 left)

South Korea used to have a higher protection for domestic rice farming mainly throughtariff and non-tariff barriers in comparison to other OECD countries (Aksoy 2005) Amongother conventional crops Korean subsidy policy focuses particularly on rice farming by sup-

18

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

Table 4 Risks adjusted revenue for the analysed period from 1996 to 2011

Crop selection Mean (million KRW) SD Sharpe ratio

Single croprice 1085 173 627

beans 596 175 340potato 3092 770 401radish 1476 298 495

cabbage 2288 435 526pepper 3294 1420 232

three-crop portfolio 2023 532 380five-crop portfolio 2412 560 430

4 Discussion

An advantage of decomposing the time series is that we can not only identify the mostfluctuating crop over time but also quantify different components of fluctuations in eachcrop Fluctuations on larger time scales (trend and seasonality) are easier for farmers toface than short-time variations which are more difficult to address in the planning processIn order to distinguish four time scales of fluctuations in each crop selection we calculatedthe ratio of eigenvalue for each time scale The ratio of eigenvalue stands for the quality ofthe reconstruction of the original time series by a certain component The larger this ratiothe more important the component will be for the reconstruction Among four time scalesthe first and the second scales can be interpreted as trend and seasonality respectively thethird and the fourth scales however were too short to be identified

Farmersrsquo decision on which crop to grow how to allocate the land to grow multiple cropsand when to harvest and sell them plays a crucial role to secure their revenue (Fafchamps1992 Kantanantha et al 2010 Klasen et al 2013) Our result showed that each crop had adifferent fluctuation pattern that highly influenced the farm revenue depending on farmersrsquocrop selection The sum of the first two ratios of eigenvalues for crop price ranged from 548(pepper) to 884 (rice) The larger the contribution of trend and seasonality the less short-time variability is contained in the data Four of the six analysed crops contained notableseasonal patterns The SSA of the three- and the five-crop portfolios also revealed thatimportant seasonal variation still remained in the monthly price data Therefore seasonalityprobably has an important impact on farmersrsquo decisions regarding the times for harvestingor marketing of their crops

The risk adjusted revenue calculated with the Sharpe ratio allows us to compare how muchrevenue standardised per 1 of revenue can be guaranteed for farmers in each crop selectionThe combination of these methods provides more information to support farmersrsquo decision oncrop selection Although the results of SSA and the Sharpe ratio showed that rice and beanfarming were the most stable they provided the lowest revenue The revenue of the three-and the five-crop portfolios was more than two times larger than in rice farming howeverat the same time the standard deviation tripled (Table 4) It indicates that the diversified

17

Time

Pric

e (U

SDto

n)

500

1000

1500

2000

1996 1998 2000 2002 2004 2006 2008 2010 2012

Korean domestic rice price World rice price

200

600

1000 original data gt 24 months (684)

Time

minus10

050

6minus24 months (154)

Time

minus10

00

100

3minus59 months (107)

Time

minus40

040

lt 29 months (54)

1991 1997 2003 2009 2015

Pric

e (U

SD

ton)

Year

Figure 7 Korean domestic rice price converted in USDton and world rice price in USDton (left) SSAdecomposition of the world rice price (right) Four groups of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it The world rice data was Thailand nominal price quote obtained from the World BankGlobal Economic Monitor (GEM) Commodities The exchange rate from Korean Won to USD for each yearwas obtained from the World Bank World Development Indicators

farming could support larger revenue This is in accordance with the study by Bhattacharyya(2008) who showed that a rice dominated farming system in India was changed to high-valuecrops for larger revenue Furthermore an analysis in Argentina showed that diversifiedfarming increased the mean return on capital with a lower coefficient of variation (Pacın andOesterheld 2014) Hence the multiple crop farming may be a means of enhancing revenue(Ali et al 2004 Winters et al 2006 Pacın and Oesterheld 2014 Rahman and Kazal 2015)However the diversification took place slowly due to agricultural subsidies concentrated ona certain crop such as rice in India (Bhattacharyya 2008) This might also be the case inSouth Korea

To examine the artificial stability of the rice price in South Korea we compared thedomestic rice price with the world rice price in USD (Figure 7) As the exchange rate variesbetween years the domestic rice price converted in USD fluctuated more compared to theone in KRW We refer to the SSA result of the rice price in KRW to keep consistency unlessmentioned While the world rice price increased drastically in 2008 as a result of the oilcrisis (Figure 7 right) the Korean domestic price was not affected by it and remained stable(Figure 3 (a)) Overall rice price in the global market fluctuates more than in the SouthKorean domestic market (Baffes and Cosic 2013) Furthermore the Korean domestic priceis more than double or triple the world price ndash the result of a substantial governmentalsupport (Figure 7 left)

South Korea used to have a higher protection for domestic rice farming mainly throughtariff and non-tariff barriers in comparison to other OECD countries (Aksoy 2005) Amongother conventional crops Korean subsidy policy focuses particularly on rice farming by sup-

18

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

Time

Pric

e (U

SDto

n)

500

1000

1500

2000

1996 1998 2000 2002 2004 2006 2008 2010 2012

Korean domestic rice price World rice price

200

600

1000 original data gt 24 months (684)

Time

minus10

050

6minus24 months (154)

Time

minus10

00

100

3minus59 months (107)

Time

minus40

040

lt 29 months (54)

1991 1997 2003 2009 2015

Pric

e (U

SD

ton)

Year

Figure 7 Korean domestic rice price converted in USDton and world rice price in USDton (left) SSAdecomposition of the world rice price (right) Four groups of fluctuation were considered larger than24 months (trend) 6ndash24 months (seasonality) 3ndash59 months smaller than 29 months The number inparenthesis shows the ratio of eigenvalues The trend component contains the mean the others show thevariability around it The world rice data was Thailand nominal price quote obtained from the World BankGlobal Economic Monitor (GEM) Commodities The exchange rate from Korean Won to USD for each yearwas obtained from the World Bank World Development Indicators

farming could support larger revenue This is in accordance with the study by Bhattacharyya(2008) who showed that a rice dominated farming system in India was changed to high-valuecrops for larger revenue Furthermore an analysis in Argentina showed that diversifiedfarming increased the mean return on capital with a lower coefficient of variation (Pacın andOesterheld 2014) Hence the multiple crop farming may be a means of enhancing revenue(Ali et al 2004 Winters et al 2006 Pacın and Oesterheld 2014 Rahman and Kazal 2015)However the diversification took place slowly due to agricultural subsidies concentrated ona certain crop such as rice in India (Bhattacharyya 2008) This might also be the case inSouth Korea

To examine the artificial stability of the rice price in South Korea we compared thedomestic rice price with the world rice price in USD (Figure 7) As the exchange rate variesbetween years the domestic rice price converted in USD fluctuated more compared to theone in KRW We refer to the SSA result of the rice price in KRW to keep consistency unlessmentioned While the world rice price increased drastically in 2008 as a result of the oilcrisis (Figure 7 right) the Korean domestic price was not affected by it and remained stable(Figure 3 (a)) Overall rice price in the global market fluctuates more than in the SouthKorean domestic market (Baffes and Cosic 2013) Furthermore the Korean domestic priceis more than double or triple the world price ndash the result of a substantial governmentalsupport (Figure 7 left)

South Korea used to have a higher protection for domestic rice farming mainly throughtariff and non-tariff barriers in comparison to other OECD countries (Aksoy 2005) Amongother conventional crops Korean subsidy policy focuses particularly on rice farming by sup-

18

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

porting direct payments and government buffer stock schemes (Park et al 2011) Especiallythe direct payment concentrated on rice farming has caused several problems including riceoverproduction and shortage of other upland field crops due to a lack of incentives (Parket al 2011) In addition our analysis on the socio-economic characteristics of farmers alsoshowed that the subsidy and the number of crops were inversely related both in PC1 andPC2 This result indicates that farmers who cultivate a small number of crops tend to receivemore subsidies and rice was the most frequently chosen crop by farmers who cultivated onecrop The government buffer stock scheme consists of purchases of commodities by the gov-ernment with the purpose of using commodity storage to stabilise prices in a whole economyas well as in an individual market (Morrow 1980) These political interventions explain whyrice is the most stable crop in South Korea

However rice policy has been influenced by external forces and will continue to changeThe Uruguay Round Agreement on Agriculture (URAA) was for instance a strong forcethat specified policy rules in 1994 (OECD 2008) Although rice farming was protected byan import ban until 1995 after the URAA it was agreed upon that a minimum market forimport would be opened and a removal of tariffs would be enacted by 2004 (Seo and Kim2005 Wailes 2005) Therefore in 2004 additional negotiations such as Doha DevelopmentAgenda (DDA) for the rice sector were inevitable Under the WTODDA negotiations forthe rice sector in South Korea Aggregate Measure of Support (AMS) by the governmentand the tariff were reduced and the market access has been increased (Park et al 2010)This can be noticed in the price data (See Supplementary Figure SF3) Actually the riceprice decreased dramatically between 2004 and 2006 Even though the government reformedthe rice policy to protect rice farmers under international treaty the amount of MinimumMarket Access (MMA) from other countries to South Korea has been set to continuouslyincrease from 225 575 tons in 2005 to 408 700 tons in 2014 (OECD 2008) Since the endof AMS in 2014 Korean government decided to open its rice market and to liberalise itfrom 2015 on (Ministry of Agriculture Food and Rural Affairs 2014) Therefore the risk offluctuating revenue for rice farmers will probably increase

Diversity loss in the agricultural landscape caused by policies has been addressed invarious studies (Potter and Burney 2002 Hollander 2004 Potter 2006) Di Falco andPerrings (2005) indicated that both crop diversity and financial support were risk-reducingstrategies for farm revenue Moreover they stressed that agricultural policy has an influencenot only on agricultural intensification as a ldquoside effectrdquo but also on farmersrsquo risk attitudeOur results suggest that the government policy for rice farming has an influence on farmersrsquodecision on crop selection which decreases the diversity of crop choice

There is a limitation to our study Even though the costs of each farming system varythe cost of management of portfolios was not taken into account for this analysis due to alack of reliable cost information on national level The risk adjusted revenue only consideredon-farm sales based on price and yield data per year We followed the assumption fromFafchamps (1992) that the farm revenue of individual crop choice was related to consumptionprices However farmers declared in the interviews that rice farming was easier and requiredfewer skills compared to cultivation of other crops This was also evident from the surveydata which showed higher costs for multi-crop farming than for single crop farming Thisdifference in portfolio management might be a critical step for farmers to adapt to new cropselections for portfolios

19

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

5 Summary and conclusions

The dynamics of global economics and climate change threaten the stability of the farmhousehold revenue Farmers as main actors to promote agricultural policy and secure foodproduction have taken several actions to minimise risks Depending on farmersrsquo decision oncrop selection crop diversity can be considered as one of strategies to stabilise their revenueand to minimise the risk under uncertainty by investing in more than one crop through theportfolio theory

We analysed the crop price and yield fluctuations for six main crops the three- and thefive-crop portfolios by Singular Spectrum Analysis (SSA) The portfolios were constructedbased on household survey data Subsequently we compared the single-crop farming withthe multiple-crop portfolios Our analysis showed that crop price and yield fluctuationscontained different components The stronger the contribution of larger time scales (namelytrend and seasonality) the less short-time variability is contained in the data Fluctuationson larger time scales (trend and seasonality) are easier for farmers to face than short-timevariations that are more difficult to address in the planning process Our results showed thateach crop has a different pattern of price and yield fluctuations Rice is the most stable cropin South Korea as its variations are mostly composed of trend and seasonality (884) andthe pepper was the most fluctuating crop (548)

Depending on their crop selection farmersrsquo revenue can vary Even though the multiplecrop farming with three and five crops did not stabilise farmersrsquo revenue compared to rice andbean farming it increased stability compared to the other crops Rice farming differs fromcultivating other crops because of external stabilisation by the governmental interferenceHowever it should be noted that the rice policy has been reformed and a high protection fordomestic rice farming would no longer last in the future Furthermore growing rice providedthe lowest revenue and farmers who cultivate several crops could as much as double theirrevenue compared to rice farming Diversified crop farming can therefore be a means ofenhancing revenue These results might have practical consequences for farmersrsquo decision-making as well as for agricultural policy

Acknowledgements

This study was carried out as part of the International Research Training Group TER-RECO (GRK 15651) funded by the Deutsche Forschungsgemeinschaft (DFG) at the Uni-versity of Bayreuth Germany and the National Research Foundation of Korea (NRF) atKangwon National University Chuncheon South Korea

References

Aksoy MA 2005 Global agricultural trade policies in Aksoy MA Beghin JC (Eds)Global Agricultural Trade and Developing Countries The World Bank Washington DCpp 37ndash53

Ali M Abedullah Farooq U 2004 Diversification with vegetables to improve competitive-ness in Asia diversification with vegetables to improve competitiveness in Asia in Ali M

20

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

(Ed) Agricultural Diversification and International Competitiveness Asian ProductivityOrganization Tokyo p 51ndash82

Allen MR Smith L 1994 Investigating the origins and significance of low-frequencymodes of climate variability Geophysical Research Letters 21 883ndash886

Awan MI van Oort PA Ahmad R Bastiaans L Meinke H 2015 Farmersrsquo viewson the future prospects of aerobic rice culture in pakistan Land Use Policy 42 517ndash526doi101016jlandusepol201409006

Baffes J Cosic D 2013 Global economic prospects Commodity markets outlook TheWorld Bank Washington DC

Below TB Mutabazi KD Kirschke D Franke C Sieber S Siebert R TscherningK 2012 Can farmersrsquo adaptation to climate change be explained by socio-economichousehold-level variables Global Environmental Change 22 223ndash235 doi101016jgloenvcha201111012

Bhattacharyya R 2008 Crop diversification A search for an alternative income of thefarmers in the state of west bengal in India in International Conference on AppliedEconomics ndash ICOAE 2008

Blank S 1990 Returns to limited crop diversification Western Journal of AgriculturalEconomics 15 204ndash212

Bradshaw B 2004 Plus crsquoest la meme chose Questioning crop diversification as a responseto agricultural deregulation in Saskatchewan Canada Journal of Rural Studies 20 35ndash48doi101016S0743-0167(03)00033-0

Bradshaw B Dolan H Smit B 2004 Farm-level adaptation to climatic variability andchange Crop diversification in the Canadian prairies Climatic Change 67 119ndash141

Brickell C 2008 RHS A-Z Encyclopedia Of Garden Plants Band 1 Dorling Kindersley

Broomhead D King GP 1986a Extracting qualitative dynamics from experimental dataPhysica D Nonlinear Phenomena 20 217ndash236 doi1010160167-2789(86)90031-X

Broomhead D King GP 1986b On the qualitative analysis of experimental dynamicalsystems in Sarkar S (Ed) Nonlinear Phenomena and Chaos Adam Hilger BristolEngland pp 113ndash114

Carew R Smith EG Grant C 2009 Factors influencing wheat yield and variabilityevidence from Manitoba Canada Journal of Agricultural and Applied Economics 41625ndash639

Castella JC Erout A 2002 Montane paddy rice the cornerstone of agricultural produc-tion systems in Bac Kan province Viet Nam in Castella JC Quang DD (Eds) DoiMoi in the Mountains Land use changes and farmersrsquo livelihood strategies in Bac KanProvince Vietnam The Agricultural Publishing House Ha Noi Viet Nam pp 175ndash195

21

Cutforth LB Francis CA Lynne GD Mortensen DA Eskridge KM 2001 Factorsaffecting farmersrsquo crop diversity decisions An integrated approach American Journal ofAlternative Agriculture 16 168ndash176 doi101017S0889189300009164

Di Falco S Bezabih M Yesuf M 2010 Seeds for livelihood Crop biodiversity and foodproduction in Ethiopia Ecological Economics 69 1695ndash1702 doi101016jecolecon201003024

Di Falco S Chavas JP 2006 Crop genetic diversity farm productivity and the man-agement of environmental risk in rainfed agriculture European Review of AgriculturalEconomics 33 289ndash314 doi101093eurragjbl016

Di Falco S Perrings C 2003 Crop genetic diversity productivity and stability of agroe-cosystems a theoretical and empirical investigation Scottish journal of political economy50 207ndash216 doi1011111467-94855002006

Di Falco S Perrings C 2005 Crop biodiversity risk management and the implicationsof agricultural assistance Ecological Economics 55 459ndash466 doi101016jecolecon200412005

van Dusen ME Taylor JE 2005 Missing markets and crop diversity evidencefrom mexico Environment and Development Economics 10 513ndash531 doi101017S1355770X05002317

Elsner JB Tsonis AA 1996 Singular spectrum analysis A new tool in time seriesanalysis Plenum Press New York

Elton E Gruber M Brown S Goetzmann W 2007 Modern portfolio theory andinvestment analysis 7 ed Wiley New York

Fader M Gerten D Krause M Lucht W Cramer W 2013 Spatial decoupling ofagricultural production and consumption quantifying dependences of countries on foodimports due to domestic land and water constraints Environmental Research Letters 8014046 doi1010881748-932681014046

Fafchamps M 1992 Cash crop production food price volatility and rural market integra-tion in the third world American Journal of Agricultural Economics 74 90ndash99 URLhttpwwwjstororgstable1242993

FAO IFAD IMF OECD UNCTAD WFP the World Bank the WTO IFPRI the UNHLTF 2011 Price Volatility in Food and Agricultural Markets Policy Responses Tech-nical Report FAO and OECD

Feola G Lerner AM Jain M Montefrio MJF Nicholas KA 2015 Research-ing farmer behaviour in climate change adaptation and sustainable agriculture Lessonslearned from five case studies Journal of Rural Studies 39 74ndash84

Gangwon-do Agricultural Research and Extensions Services 2016 httpwwwares

gangwonkrhbensub01_04 Accessed in June 2016

22

Gangwon Province 2016 httpwwwprovingangwonkrgwportalsub03_01 In Ko-rean Accessed in June 2016

Gaydon D Meinke H Rodriguez D McGrath D 2012 Comparing water options forirrigation farmers using modern portfolio theory Agricultural Water Management 1151ndash9 doi101016jagwat201208007

Golyandina N Korobeynikov A 2013 Basic singular spectrum analysis and forecastingwith r Computational Statistics amp Data Analysis 71 934ndash954 doi101016jcsda201304009

Golyandina N Nekrutkin V Zhigljavsky AA 2001 Analysis of time series structureSSA and related techniques Chapman amp HallCRC Boca Raton Fla

Golyandina N Zhigljavsky A 2013 Singular spectrum analysis for time series Springer

Gopikrishnan P Rosenow B Plerou V Stanley H 2001 Quantifying and interpretingcollective behavior in financial markets Physical Review E 64 035106 doi101103PhysRevE64035106

Guvele C 2001 Gains from crop diversification in the sudan gezira scheme AgriculturalSystems 70 319ndash333

Halpern BS White C Lester SE Costello C Gaines SD 2011 Using portfoliotheory to assess tradeoffs between return from natural capital and social equity acrossspace Biological Conservation 144 1499ndash1507 doi101016jbiocon201101019

Han G Kim T 2010 Causes of recent cabbage shock and policy implications (in Korean)volume 255 of CEO focus Nonghyup Economic Research Institute 15

Harvey CA Rakotobe ZL Rao NS Dave R Razafimahatratra H Rabarijohn RHRajaofara H MacKinnon JL 2014 Extreme vulnerability of smallholder farmers toagricultural risks and climate change in madagascar Philosophical Transactions B of theRoyal Society 369 20130089 doi101098rstb20130089

Hassani H Thomakos D 2010 A review on singular spectrum analysis for economic andfinancial time series Statistics and its Interface 3 377ndash397

Heady EO 1952 Diversification in resource allocation and minimization of income vari-ability Journal of Farm Economics 34 482ndash496

Herrero M Thornton PK Bernues A Baltenweck I Vervoort J van de Steeg JMakokha S van Wijk MT Karanja S Rufino MC Staal SJ 2014 Exploringfuture changes in smallholder farming systems by linking socio-economic scenarios withregional and household models Global Environmental Change 24 165ndash182 doi101016jgloenvcha201312008

Hollander GM 2004 Agricultural trade liberalization multifunctionality and sugar in thesouth Florida landscape Themed issue on rsquoneoliberal nature and the nature of neoliber-alismrsquo Geoforum 35 299ndash312 doi101016jgeoforum200311004

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Hong S Kim S Kim J 2003 Implications of potential green tourism developmentAnnals of Tourism Research 30 323ndash341 doi101016S0160-7383(02)00060-9

Ilbery BW 1978 Agricultural decision-making a behavioural perspective Progress inHuman Geography 2 448ndash466

Janssen S van Ittersum MK 2007 Assessing farm innovations and responses to policiesA review of bio-economic farm models Agricultural Systems 94 622ndash636 doi101016jagsy200703001

Just RE Pope RD 1978 Stochastic specification of production functions and economicimplications Journal of Econometrics 7 67ndash86 doi1010160304-4076(78)90006-4

Kang M Kang S Ryu C 2010 A study on climate change in gangwon-province (inKorean) Proceedings of the Korean Environmental Sciences Society Conference 19 139ndash141

Kantanantha N Serban N Griffin P 2010 Yield and price forecasting for stochasticcrop decision planning Journal of Agricultural Biological and Environmental Statistics15 362ndash380 doi101007s13253-010-0025-7

Kim C Lee S Jeong H Jang J Kim Y Lee C 2010 Impacts of Climate Changeon Korean Agriculture and Its Counterstrategies Research Report R593 Korea RuralEconomic Institute Seoul

Kim S Yang J Park C Jung Y Cho B 2007 Effects of winter cover crop of ryegrass(lolium multiflorum) and soil conservation practices on soil erosion and quality in thesloping uplands Journal of Applied Biological Chemistry 50 22ndash28

Kiyono K Struzik Z Yamamoto Y 2006 Criticality and phase transition in stock-pricefluctuations Physical Review Letters 96 068701 doi101103PhysRevLett96068701

Klasen S Priebe J Rudolf R 2013 Cash crop choice and income dynamics in ruralareas evidence for post-crisis indonesia Agricultural Economics 44 349ndash364 doi101111agec12015

Koellner T Schmitz OJ 2006 Biodiversity ecosystem function and investment riskBioScience 56 977ndash985 doi1016410006-3568(2006)56[977BEFAIR]20CO2

Korea Rural Economic Institute 2015 Agriculture in Korea Korea Rural Economic Insti-tute

Korobeynikov A 2010 Computation- and space-efficient implementation of SSA Statisticsand Its Interface 3 357ndash368 R package version 099

Kristensen SP Thenail C Kristensen L 2001 Farmersrsquo involvement in landscape ac-tivities An analysis of the relationship between farm location farm characteristics andlandscape changes in two study areas in jutland denmark Journal of EnvironmentalManagement 61 301ndash318 doi101006jema20000409

24

Kwon W 2012 Climate change scenario and applications in agriculture (in Korean)in Korea Rural Economic Institute (Ed) Agricultural Outlook Korea Rural EconomicInstitute Seoul E04-2012 pp 997ndash1026

Lavorel S Grigulis K Lamarque P Colace MP Garden D Girel J Pellet GDouzet R 2011 Using plant functional traits to understand the landscape distribu-tion of multiple ecosystem services Journal of Ecology 99(1) 135ndash147 doi101111j1365-2745201001753x

Lien G Hardaker J 2001 Whole-farm planning under uncertainty impacts of subsidyscheme and utility function on portfolio choice in Norwegian agriculture European Reviewof Agricultural Economics 28 17ndash36 doi101093erae28117

Liu Y Gopikrishnan P Cizeau P Meyer M Peng CK Stanley HE 1999 Statisticalproperties of the volatility of price fluctuations Physical Review E 60 1390ndash1400 doi101103PhysRevE601390

Mahecha MD Reichstein M Jung M Seneviratne SI Zaehle S Beer C BraakhekkeMC Carvalhais N Lange H Le Maire G Moors E 2010 Comparing observationsand process-based simulations of biosphere-atmosphere exchanges on multiple timescalesJournal of Geophysical Research 115 G02003 doi1010292009JG001016

Markowitz H 1952 Portfolio selection The Journal of Finance 7 77ndash91 doi101111j1540-62611952tb01525x

Ministry of Agriculture Food and Rural Affairs 2014 httpwwwmafragokrrice

0101_03html In Korean Accessed in June 2016

Mishra AK El-Osta HS Morehart MJ Johnson JD Hopkins JW 2002 IncomeWealth and the Economic Well-Being of Farm Households Agricultural Economic Report812 US Department of Agriculture Washington DC 1800 M Street NW WashingtonDC 20036-5831

Morrow Daniel T 1980 The economics of the international Stockholding of wheat Inter-national Food Policy Research Institute

OECD 2008 Evaluation of Agricultural Policy Reforms in Korea Technical Report OECDParis

Olesen J Trnka M Kersebaum K Skjelvag A Seguin B Peltonen-Sainio P RossiF Kozyra J Micale F 2011 Impacts and adaptation of European crop productionsystems to climate change European Journal of Agronomy 34 96ndash112 doi101016jeja201011003

Pacın F Oesterheld M 2014 In-farm diversity stabilizes return on capital in argentineagro-ecosystems Agricultural Systems 124 51ndash59 doi101016jagsy201310008

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Park D Kim M Park M Sa G Kim G 2010 Debate for the development of the riceindustry (in Korean) Number D287 in Research Report Korea Rural Economic InstituteSeoul

Park S Park J Song J Chae G Moon H 2011 Research on agricultural subsidyrefrom (in Korean) P140 Korea Rural Economic Institute

Pellegrini L Tasciotti L 2014 Crop diversification dietary diversity and agriculturalincome empirical evidence from eight developing countries Canadian Journal of De-velopment StudiesRevue canadienne drsquoetudes du developpement 211ndash227doi101080022551892014898580

Potter C 2006 Competing narratives for the future of European agriculture The agri-environmental consequences of neoliberalization in the context of the Doha round TheGeographical Journal 172 190ndash196 URL httpwwwjstororgstable3873962

Potter C Burney J 2002 Agricultural multifunctionality in the WTOmdashlegitimate non-trade concern or disguised protectionism Journal of Rural Studies 18 35ndash47 doi101016S0743-0167(01)00031-6

Potter C Lobley M 1992 The conservation status and potential of elderly farmersResults from a survey in england and wales Journal of Rural Studies 8 133ndash143 doi1010160743-0167(92)90072-E

R Core Team 2013 R A Language and Environment for Statistical Computing R Foun-dation for Statistical Computing Vienna Austria URL httpwwwR-projectorg

Radulescu M Radulescu CZ Zbaganu G 2014 A portfolio theory approach to cropplanning under environmental constraints Annlas of Operations Research 219 243ndash264doi101007s10479-011-0902-7

Rahman S 2009 Whether crop diversification is a desired strategy for agricultural growthin Bangladesh Food Policy 34 340ndash349

Rahman S Kazal MMH 2015 Determinants of crop diversity in the regions ofbangladesh (1990ndash2008) Singapore Journal of Tropical Geography 36 83ndash97

Robison LJ Brake JR 1979 Application of portfolio theory to farmer and lenderbehavior American Journal of Agricultural Economics 61 URL httpwwwjstororgstable1239520

Roche MJ McQuinn K 2004 Riskier product portfolio under decoupled paymentsEuropean Review of Agricultural Economics 31 111ndash123

Rome Declaration on World Food Security and World Food Summit Plan of Action 1996URL httpwwwfaoorgDOCREP003W3613EW3613E00HTM

Schaefer S 2013 The South Korean adaptation actor-network in the agricultural sectorPhD thesis University of Bayreuth

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Seo J Kim B 2005 Forecast and challenges of Korea rice farming after the rice negotiation(in Korean) in Oh SI (Ed) Agriculture Forecast (I) Korea Rural Economic Institutepp 57ndash79

Sharpe WF 1994 The sharpe ratio The Journal of Portfolio Management 21 49ndash58doi103905jpm1994409501

Smale M Hartell J Heisey PW Senauer B 1998 The contribution of genetic re-sources and diversity to wheat production in the Punjab of Pakistan American Journalof Agricultural Economics 80 482ndash493 URL httpwwwjstororgstable1244551

Talkner P Weber RO 2000 Power spectrum and detrended fluctuation analysis Ap-plication to daily temperatures Physical Review E 62 150ndash160 doi101103PhysRevE62150

Thomakos DD Wang T Wille LT 2002 Modeling daily realized futures volatilitywith singular spectrum analysis Physica A Statistical Mechanics and its Applications312 505ndash519 doi101016S0378-4371(02)00845-2

Tilman D Reich PB Knops JMH 2006 Biodiversity and ecosystem stability in adecade-long grassland experiment Nature 441 629ndash632 doi101038nature04742

USDA 2007 Soybean Objective Yield Survey Data 1992-2006 Technical Report theNational Agricultural Statistics Service (NASS) Agricultural Statistics Board US De-partment of Agriculture

Vianna ML Menezes VV 2006 Singular spectrum analysis of nonstationary tidal cur-rents applied to ADCP data from the Northeast Brazilian shelf Journal of Atmosphericand Oceanic Technology 23 138ndash151 doi101175JTECH18241

Wailes EJ 2005 Rice Global trade protectionist policies and the impact of tradelibralization in Aksoy MA Beghin J (Eds) Global Agricultural Trade and DevelopingCountries The World Bank Washington DC pp 177ndash193

Wang J Mendelsohn R Dinar A Huang J 2010 How Chinese farmers change cropchoice to adapt to climate change Climate Change Economics 1 167ndash185 doi101142S2010007810000145

Winters P Cavatassi R Lipper L 2006 Sowing the Seeds of Social Relations The Roleof Social Capital in Crop Diversity ESA Working Paper 06-16 The Food and AgricultureOrganization of the United Nations Rome Italy

Wood SA Jina AS Jain M Kristjanson P DeFries RS 2014 Smallholder farmercropping decisions related to climate variability across multiple regions Global Environ-mental Change 25 163ndash172 doi101016jgloenvcha201312011

27